First- or Corresponding-Author Articles¶
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- The publication list is automatically generated from bibtex by using bibtex2html.py that I developed.
- # denotes co-first authors. * denotes corresponding authors.
• Total Citations: 1773 • H-Index: 22
• TMI (5) • MedIA (1) • NeuroImage (1) • HBM (1) • CC (1) • MICCAI (13) • IPMI (2) •
• Book Chapters • Journals • Conferences • Abstracts • Theses •
Book Chapters¶
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Jian Cheng, Hongtu Zhu,
"Diffusion Magnetic Resonance Imaging (dMRI)",
Handbook of Neuroimaging Data Analysis, 2016.![[pdf]](Icons/pdf.gif)
![[www]](Icons/www.gif)
[bibtex]
[abstract]
[citations: 4]
Bibtex
@inbook{cheng:handbook2016, author = {Jian Cheng and Hongtu Zhu}, booktitle = {Handbook of Neuroimaging Data Analysis}, hal_id = {hal-01430475}, pdf = {https://hal.archives-ouvertes.fr/hal-01430475/document}, title = {Diffusion Magnetic Resonance Imaging (dMRI)}, url = {https://hal.archives-ouvertes.fr/hal-01430475}, year = {2016} }Abstract
Since the 1980s, diffusion magnetic resonance imaging (dMRI) as a magnetic resonance imaging (MRI) technique has been widely used to track the effective diffusion of water molecules, which is hindered by many obstacles (e.g., fibers or membranes), in the human brain in vivo. Because water molecules tend to diffuse slowly across white matter fibers and diffuse fast along such fibers, the use of dMRI to track water diffusion allows one to map the microstructure and organization of those white matter pathways (17). Quantitatively measuring the diffusion process is critical for a quantitative assessment of the integrity of anatomical connectivity in white matter and its association with brain functional connectivity. Its clinical applications include normal brain maturation and aging, cerebral ischemia, multiple sclerosis, epilepsy, metabolic disorders, and brain tumors, among many others. Although there are several nice review papers and monographies on dMRI (15, 5, 101, 81), this chapter was written for the readers who are interested in the theoretical underpinning of various mathematical and statistical methods associated with dMRI. Due to limitations of space, we are unable to cite all important papers in the dMRI literature.
Journal Articles¶
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Xiaolin Fan, Yan Wang, Yingying Zhang*, Mingkun Bao, Bosen Jia, Dong Lu, Yifan Gu, Jian Cheng*, Haogang Zhu*,
"AVP-AP: Self-supervised Automatic View Positioning in 3D cardiac CT via Atlas Prompting",
IEEE Transactions on Medical Imaging (TMI), 2025.
[bibtex]
[abstract]
[arxiv]
Bibtex
@article{fan:AVP-AP:TMI2025, author = {Xiaolin Fan and Yan Wang and Yingying Zhang and Mingkun Bao and Bosen Jia and Dong Lu and Yifan Gu and Jian Cheng and Haogang Zhu}, doi = {10.1109/TMI.2025.3554785}, journal = {IEEE Transactions on Medical Imaging}, pdf = {https://arxiv.org/pdf/2504.05966.pdf}, publisher = {IEEE}, title = {AVP-AP: Self-supervised Automatic View Positioning in 3D cardiac CT via Atlas Prompting}, url = {https://dx.doi.org/10.1109/TMI.2025.3554785}, year = {2025} }Abstract
Automatic view positioning is crucial for cardiac computed tomography (CT) examinations, including disease diagnosis and surgical planning. However, it is highly challenging due to individual variability and large 3D search space. Existing work needs labor-intensive and time-consuming manual annotations to train view-specific models, which are limited to predicting only a fixed set of planes. However, in real clinical scenarios, the challenge of positioning semantic 2D slices with any orientation into varying coordinate space in arbitrary 3D volume remains unsolved. We thus introduce a novel framework, AVP-AP, the first to use Atlas Prompting for self-supervised Automatic View Positioning in the 3D CT volume. Specifically, this paper first proposes an atlas prompting method, which generates a 3D canonical atlas and trains a network to map slices into their corresponding positions in the atlas space via a self-supervised manner. Then, guided by atlas prompts corresponding to the given query images in a reference CT, we identify the coarse positions of slices in the target CT volume using rigid transformation between the 3D atlas and target CT volume, effectively reducing the search space. Finally, we refine the coarse positions by maximizing the similarity between the predicted slices and the query images in the feature space of a given foundation model. Our framework is flexible and efficient compared to other methods, outperforming other methods by 19.8% average structural similarity (SSIM) in arbitrary view positioning and achieving 9% SSIM in two-chamber view compared to four radiologists. Meanwhile, experiments on a public dataset validate our framework's generalizability.
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Shaodong Ding, Ziyang Liu, Pan Liu, Wanlin Zhu, Hong Xu, Zixiao Li, Haijun Niu, Jian Cheng*, Tao Liu*,
"C3R: Category contrastive adaptation and consistency regularization for cross-modality medical image segmentation",
Expert Systems with Applications, vol. 269, pp. 126304, 2025.
[bibtex]
[abstract]
Bibtex
@article{ding2025c3r, author = {Shaodong Ding and Ziyang Liu and Pan Liu and Wanlin Zhu and Hong Xu and Zixiao Li and Haijun Niu and Jian Cheng and Tao Liu}, doi = {h10.1016/j.eswa.2024.126304}, journal = {Expert Systems with Applications}, pages = {126304}, publisher = {Elsevier}, title = {C3R: Category contrastive adaptation and consistency regularization for cross-modality medical image segmentation}, url = {https://dx.doi.org/h10.1016/j.eswa.2024.126304}, volume = {269}, year = {2025} }Abstract
Unsupervised Domain Adaptation (UDA) has been widely used in cross- modality medical image segmentation, where the segmentation network is trained using both labeled images from the source domain and unlabeled images from the target domain. A prominent research direction in UDA involves learning domain-invariant features through image translation between the source and target domain images, typically utilizing cycle consistency loss and/or adversarial loss. However, we argue that the auxiliary cycle consistency loss and adversarial loss may interfere with the main segmentation loss during training, despite its utility in learning domain-invariant features. Furthermore, existing approaches in this research direction overlook the differentiation of various categories in domain-invariant feature learning. In this paper, we propose a novel UDA method, named C3R, for medical image segmentation. C3R mainly comprises four components: a shared encoder for learning domain- invariant features, a segmenter for generating segmentation output, and two decoders for image translation between the source and target domains. C3R fully explores consistency regularization in training, including image-level consistency, feature-level consistency, and segmentation output-level consistency. Moreover, C3R employs a detached training strategy to alleviate conflict between the main segmentation loss and auxiliary cycle consistency loss and adversarial loss. Last, C3R applies contrastive learning to pull together pixels of the same category, while pushing apart pixels of different categories, thereby enhancing the final segmentation results. Experimental results show that C3R outperforms other state- of-the-art methods by a considerable margin in Dice: 2.25% in cardiac substructure segmentation, 7.98% in brain tumor segmentation, and 1.8% in abdominal multi-organ segmentation.
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Jianyu Li#, Jian Cheng#, Lei Yang#, Qihui Niu*, Yuanchao Zhang*, Lena Palaniyappan,
"Association of cortical gyrification, white matter microstructure, and phenotypic profile in medication-naïve obsessive–compulsive disorder",
Psychological Medicine, vol. 54, no. 8, pp. 1573–1579, 2024.
[bibtex]
[abstract]
[citations: 2]
Bibtex
@article{li_cheng_yang_niu_zhang_palaniyappan_2023, author = {Jianyu Li and Jian Cheng and Lei Yang and Qihui Niu and Yuanchao Zhang and Lena Palaniyappan}, doi = {10.1017/S0033291723003422}, journal = {Psychological Medicine}, number = {8}, pages = {1573-1579}, publisher = {Cambridge University Press}, title = {Association of cortical gyrification, white matter microstructure, and phenotypic profile in medication-naïve obsessive–compulsive disorder}, url = {https://dx.doi.org/10.1017/S0033291723003422}, volume = {54}, year = {2024} }Abstract
Background Obsessive–compulsive disorder (OCD) is thought to arise from dysconnectivity among interlinked brain regions resulting in a wide spectrum of clinical manifestations. Cortical gyrification, a key morphological feature of human cerebral cortex, has been considered associated with developmental connectivity in early life. Monitoring cortical gyrification alterations may provide new insights into the developmental pathogenesis of OCD. Methods Sixty- two medication-naive patients with OCD and 59 healthy controls (HCs) were included in this study. Local gyrification index (LGI) was extracted from T1-weighted MRI data to identify the gyrification changes in OCD. Total distortion (splay, bend, or twist of fibers) was calculated using diffusion-weighted MRI data to examine the changes in white matter microstructure in patients with OCD. Results Compared with HCs, patients with OCD showed significantly increased LGI in bilateral medial frontal gyrus and the right precuneus, where the mean LGI was positively correlated with anxiety score. Patients with OCD also showed significantly decreased total distortion in the body, genu, and splenium of the corpus callosum (CC), where the average distortion was negatively correlated with anxiety scores. Intriguingly, the mean LGI of the affected cortical regions was significantly correlated with the mean distortion of the affected white matter tracts in patients with OCD. Conclusions We demonstrated associations among increased LGI, aberrant white matter geometry, and higher anxiety in patients with OCD. Our findings indicate that developmental dysconnectivity-driven alterations in cortical folding are one of the neural substrates underlying the clinical manifestations of OCD.
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Yuwen Wang, Mingxiu Han, Yudan Peng, Ruoqi Zhao, Dongqiong Fan, Xia Meng, Hong Xu, Haijun Niu, Jian Cheng*, Tao Liu*,
"LGNet: Learning local--global EEG representations for cognitive workload classification in simulated flights",
Biomedical Signal Processing and Control, vol. 92, pp. 106046, 2024.
[bibtex]
[abstract]
[citations: 11]
Bibtex
@article{wang2024lgnet, author = {Yuwen Wang and Mingxiu Han and Yudan Peng and Ruoqi Zhao and Dongqiong Fan and Xia Meng and Hong Xu and Haijun Niu and Jian Cheng and Tao Liu}, doi = {10.1016/j.bspc.2024.106046}, journal = {Biomedical Signal Processing and Control}, pages = {106046}, publisher = {Elsevier}, title = {LGNet: Learning local--global EEG representations for cognitive workload classification in simulated flights}, url = {https://dx.doi.org/10.1016/j.bspc.2024.106046}, volume = {92}, year = {2024} }Abstract
Cognitive workload assessment is crucial for ensuring pilots' safety during flights. Electroencephalography (EEG) is a promising tool for monitoring cognitive workload. Convolutional neural networks (CNNs) are effective in automatically extracting local EEG representations. However, CNNs have limitations in global representations, because a global representation in CNNs normally requires CNNs to be deep enough to have a global receptive field, which normally results in overfitting. To address this issue, we propose a local and global network (LGNet) for assessing two levels of cognitive workload based on EEG during simulated flight. We fuse convolutional and Transformer layers to extract local and global representations from the EEG signals. To enhance the learning performance, we propose a novel SCCE loss, which combines the supervised contrastive loss with the traditional cross-entropy loss. We collect 32-channel EEG data from 10 subjects who perform low and high cognitive workload flight tasks with passive auditory stimuli in a flight simulator on 3 separate days, with each participant performing the task for approximately 345 min. The results show that LGNet with the SCCE loss achieves a 4-fold average classification accuracy of 91.19 % based on cross-clip data partitioning and an average classification accuracy of 83.26 % based on cross-session data partitioning when no target session data is added to the training data. These results significantly outperform classifiers based on handcrafted features and state-of-the-art deep learning methods.
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Yuwen Wang#, Yudan Peng#, Mingxiu Han, Xinyi Liu, Haijun Niu, Jian Cheng*, Suhua Chang*, Tao Liu*,
"GCTNet: a graph convolutional transformer network for major depressive disorder detection based on EEG signals",
Journal of Neural Engineering, vol. 21, no. 3, pp. 036042, jun, 2024.
[bibtex]
[abstract]
[citations: 4]
Bibtex
@article{Wang_JNE2024, author = {Yuwen Wang and Yudan Peng and Mingxiu Han and Xinyi Liu and Haijun Niu and Jian Cheng and Suhua Chang and Tao Liu}, doi = {10.1088/1741-2552/ad5048}, journal = {Journal of Neural Engineering}, month = {jun}, number = {3}, pages = {036042}, publisher = {IOP Publishing}, title = {GCTNet: a graph convolutional transformer network for major depressive disorder detection based on EEG signals}, url = {http://iopscience.iop.org/article/10.1088/1741-2552/ad5048}, volume = {21}, year = {2024} }Abstract
Objective. Identifying major depressive disorder (MDD) using objective physiological signals has become a pressing challenge. Approach. Hence, this paper proposes a graph convolutional transformer network (GCTNet) for accurate and reliable MDD detection using electroencephalogram (EEG) signals. The developed framework integrates a residual graph convolutional network (ResGCN) block to capture spatial information and a Transformer block to extract global temporal dynamics. Additionally, we introduce the contrastive cross-entropy (CCE) loss that combines contrastive learning to enhance the stability and discriminability of the extracted features, thereby improving classification performance. Main results. The effectiveness of the GCTNet model and CCE loss was assessed using EEG data from 41 MDD patients and 44 normal controls (NC), in addition to a publicly available dataset. Utilizing a subject-independent data partitioning method and 10-fold cross- validation, the proposed method demonstrated significant performance, achieving an average Area Under the Curve (AUC) of 0.7693 and 0.9755 across both datasets, respectively. Comparative analyses demonstrated the superiority of the GCTNet framework with CCE loss over state-of-the-art algorithms in MDD detection tasks. Significance. The proposed method offers an objective and effective approach to MDD detection, providing valuable support for clinical- assisted diagnosis.
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Keyi He, Bo Peng, Weibo Yu, Yan Liu, Surui Liu, Jian Cheng*, Yakang Dai*,
"A Novel Mis-Seg-Focus Loss Function Based on a Two-Stage nnU-Net Framework for Accurate Brain Tissue Segmentation",
Bioengineering, vol. 11, no. 5, pp. 427, 2024.
[bibtex]
[abstract]
Bibtex
@article{he2024novel, author = {Keyi He and Bo Peng and Weibo Yu and Yan Liu and Surui Liu and Jian Cheng and Yakang Dai}, doi = {10.3390/bioengineering11050427}, journal = {Bioengineering}, number = {5}, pages = {427}, publisher = {MDPI}, title = {A Novel Mis-Seg-Focus Loss Function Based on a Two-Stage nnU-Net Framework for Accurate Brain Tissue Segmentation}, url = {https://dx.doi.org/10.3390/bioengineering11050427}, volume = {11}, year = {2024} }Abstract
Brain tissue segmentation plays a critical role in the diagnosis, treatment, and study of brain diseases. Accurately identifying these boundaries is essential for improving segmentation accuracy. However, distinguishing boundaries between different brain tissues can be challenging, as they often overlap. Existing deep learning methods primarily calculate the overall segmentation results without adequately addressing local regions, leading to error propagation and mis-segmentation along boundaries. In this study, we propose a novel mis-segmentation-focused loss function based on a two-stage nnU-Net framework. Our approach aims to enhance the model’s ability to handle ambiguous boundaries and overlapping anatomical structures, thereby achieving more accurate brain tissue segmentation results. Specifically, the first stage targets the identification of mis-segmentation regions using a global loss function, while the second stage involves defining a mis- segmentation loss function to adaptively adjust the model, thus improving its capability to handle ambiguous boundaries and overlapping anatomical structures. Experimental evaluations on two datasets demonstrate that our proposed method outperforms existing approaches both quantitatively and qualitatively.
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Yan Wang, Jian Cheng*, Yixin Chen, Shuai Shao, Lanyun Zhu, Zhenzhou Wu, Tao Liu, Haogang Zhu*,
"FVP: Fourier Visual Prompting for Source-Free Unsupervised Domain Adaptation of Medical Image Segmentation",
IEEE Transactions on Medical Imaging (TMI), vol. 42, no. 12, pp. 3738–3751, 2023.
[bibtex]
[abstract]
[arxiv]
[citations: 33]
Bibtex
@article{wang2023fvp, author = {Yan Wang and Jian Cheng and Yixin Chen and Shuai Shao and Lanyun Zhu and Zhenzhou Wu and Tao Liu and Haogang Zhu}, doi = {10.1109/TMI.2023.3306105}, journal = {IEEE Transactions on Medical Imaging}, number = {12}, pages = {3738-3751}, pdf = {https://arxiv.org/pdf/2304.13672.pdf}, title = {FVP: Fourier Visual Prompting for Source-Free Unsupervised Domain Adaptation of Medical Image Segmentation}, url = {https://dx.doi.org/10.1109/TMI.2023.3306105}, volume = {42}, year = {2023} }Abstract
Medical image segmentation methods normally perform poorly when there is a domain shift between training and testing data. Unsupervised Domain Adaptation (UDA) addresses the domain shift problem by training the model using both labeled data from the source domain and unlabeled data from the target domain. Source-Free UDA (SFUDA) was recently proposed for UDA without requiring the source data during the adaptation, due to data privacy or data transmission issues, which normally adapts the pre-trained deep model in the testing stage. However, in real clinical scenarios of medical image segmentation, the trained model is normally frozen in the testing stage. In this paper, we propose Fourier Visual Prompting (FVP) for SFUDA of medical image segmentation. Inspired by prompting learning in natural language processing, FVP steers the frozen pre-trained model to perform well in the target domain by adding a visual prompt to the input target data. In FVP, the visual prompt is parameterized using only a small amount of low-frequency learnable parameters in the input frequency space, and is learned by minimizing the segmentation loss between the predicted segmentation of the prompted target image and reliable pseudo segmentation label of the target image under the frozen model. To our knowledge, FVP is the first work to apply visual prompts to SFUDA for medical image segmentation. The proposed FVP is validated using three public datasets, and experiments demonstrate that FVP yields better segmentation results, compared with various existing methods.
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Haichao Zhao, Wei Wen, Jian Cheng*, Jiyang Jiang, Nicole Kochan, Haijun Niu, Henry Brodaty, Perminder Sachdev, Tao Liu*,
"An accelerated degeneration of white matter microstructure and networks in the nondemented old–old",
Cerebral Cortex (CC), vol. 33, no. 8, pp. 4688–4698, 2023.
[bibtex]
[abstract]
[citations: 8]
Bibtex
@article{zhao:DFA:CC2022, author = {Haichao Zhao and Wei Wen and Jian Cheng and Jiyang Jiang and Nicole Kochan and Haijun Niu and Henry Brodaty and Perminder Sachdev and Tao Liu}, doi = {10.1093/cercor/bhac372}, journal = {Cerebral Cortex}, number = {8}, pages = {4688-4698}, pdf = {https://academic.oup.com/cercor/advance-article-pdf/doi/10.1093/cercor/bhac372/46212258/bhac372.pdf}, publisher = {Oxford University Press}, title = {An accelerated degeneration of white matter microstructure and networks in the nondemented old–old}, url = {https://doi.org/10.1093/cercor/bhac372}, volume = {33}, year = {2023} }Abstract
{The nondemented old–old over the age of 80 comprise a rapidly increasing population group; they can be regarded as exemplars of successful aging. However, our current understanding of successful aging in advanced age and its neural underpinnings is limited. In this study, we measured the microstructural and network-based topological properties of brain white matter using diffusion- weighted imaging scans of 419 community-dwelling nondemented older participants. The participants were further divided into 230 young–old (between 72 and 79, mean = 76.25 ± 2.00) and 219 old–old (between 80 and 92, mean = 83.98 ± 2.97). Results showed that white matter connectivity in microstructure and brain networks significantly declined with increased age and that the declined rates were faster in the old–old compared with young–old. Mediation models indicated that cognitive decline was in part through the age effect on the white matter connectivity in the old–old but not in the young–old. Machine learning predictive models further supported the crucial role of declines in white matter connectivity as a neural substrate of cognitive aging in the nondemented older population. Our findings shed new light on white matter connectivity in the nondemented aging brains and may contribute to uncovering the neural substrates of successful brain aging.} -
Ruoqi Zhao, Yuwen Wang, Xiangxin Cheng, Wanlin Zhu, Xia Meng, Haijun Niu, Jian Cheng*, Tao Liu*,
"A mutli-scale spatial-temporal convolutional neural network with contrastive learning for motor imagery EEG classification",
Medicine in Novel Technology and Devices, vol. 17, pp. 100215, 2023.
[bibtex]
[abstract]
[citations: 13]
Bibtex
@article{ZHAO2023100215, author = {Ruoqi Zhao and Yuwen Wang and Xiangxin Cheng and Wanlin Zhu and Xia Meng and Haijun Niu and Jian Cheng and Tao Liu}, doi = {https://doi.org/10.1016/j.medntd.2023.100215}, journal = {Medicine in Novel Technology and Devices}, pages = {100215}, title = {A mutli-scale spatial-temporal convolutional neural network with contrastive learning for motor imagery EEG classification}, url = {https://www.sciencedirect.com/science/article/pii/S2590093523000103}, volume = {17}, year = {2023} }Abstract
Motor imagery (MI) based Brain-computer interfaces (BCIs) have a wide range of applications in the stroke rehabilitation field. However, due to the low signal-to-noise ratio and high cross-subject variation of the electroencephalogram (EEG) signals generated by motor imagery, the classification performance of the existing methods still needs to be improved to meet the need of real practice. To overcome this problem, we propose a multi-scale spatial-temporal convolutional neural network called MSCNet. We introduce the contrastive learning into a multi-temporal convolution scale backbone to further improve the robustness and discrimination of embedding vectors. Experimental results of binary classification show that MSCNet outperforms the state-of-the-art methods, achieving accuracy improvement of 6.04%, 3.98%, and 8.15% on BCIC IV 2a, SMR- BCI, and OpenBMI datasets in subject-dependent manner, respectively. The results show that the contrastive learning method can significantly improve the classification accuracy of motor imagery EEG signals, which provides an important reference for the design of motor imagery classification algorithms.
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Jian Cheng#, Ziyang Liu#, Hao Guan, Zhenzhou Wu, Haogang Zhu, Jiyang Jiang, Wei Wen, Dacheng Tao, Tao Liu*,
"Brain Age Estimation From MRI Using Cascade Networks with Ranking Loss",
IEEE Transactions on Medical Imaging (TMI), vol. 40, no. 12, pp. 3400–3412, 2021.
[bibtex]
[abstract]
[arxiv]
[code]
[citations: 75]
(Jian Cheng and Ziyang Liu contributed equally.)
Bibtex
@article{cheng:TMI2021, author = {Jian Cheng and Ziyang Liu and Hao Guan and Zhenzhou Wu and Haogang Zhu and Jiyang Jiang and Wei Wen and Dacheng Tao and Tao Liu}, doi = {10.1109/TMI.2021.3085948}, journal = {IEEE Transactions on Medical Imaging}, number = {12}, pages = {3400-3412}, pdf = {https://arxiv.org/pdf/2106.03052.pdf}, publisher = {IEEE}, title = {Brain Age Estimation From MRI Using Cascade Networks with Ranking Loss}, url = {https://dx.doi.org/10.1109/TMI.2021.3085948}, volume = {40}, year = {2021} }Abstract
Chronological age of healthy people is able to be predicted accurately using deep neural networks from neuroimaging data, and the predicted brain age could serve as a biomarker for detecting aging-related diseases. In this paper, a novel 3D convolutional network, called two-stage-age-network (TSAN), is proposed to estimate brain age from T1-weighted MRI data. Compared with existing methods, TSAN has the following improvements. First, TSAN uses a two-stage cascade network architecture, where the first-stage network estimates a rough brain age, then the second-stage network estimates the brain age more accurately from the discretized brain age by the first-stage network. Second, to our knowledge, TSAN is the first work to apply novel ranking losses in brain age estimation, together with the traditional mean square error (MSE) loss. Third, densely connected paths are used to combine feature maps with different scales. The experiments with $6586$ MRIs showed that TSAN could provide accurate brain age estimation, yielding mean absolute error (MAE) of $2.428$ and Pearson's correlation coefficient (PCC) of $0.985$, between the estimated and chronological ages. Furthermore, using the brain age gap between brain age and chronological age as a biomarker, Alzheimer's disease (AD) and Mild Cognitive Impairment (MCI) can be distinguished from healthy control (HC) subjects by support vector machine (SVM). Classification AUC in AD/HC and MCI/HC was $0.904$ and $0.823$, respectively. It showed that brain age gap is an effective biomarker associated with risk of dementia, and has potential for early-stage dementia risk screening. The codes and trained models have been released on GitHub: https://github.com/Milan-BUAA/TSAN- brain-age-estimation.
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Haichao Zhao#, Jian Cheng#, Tao Liu*, Jiyang Jiang, Forrest Koch, Perminder S. Sachdev, Peter J. Basser, Wei Wen, for the Alzheimer's Disease Neuroimaging Initiative,
"Orientational changes of white matter fibers in Alzheimer's disease and amnestic mild cognitive impairment",
Human Brain Mapping (HBM), 2021.
[bibtex]
[abstract]
[citations: 14]
(Haichao Zhao and Jian Cheng contributed equally.)
Bibtex
@article{zhao:DFA:HBM2021, author = {Haichao Zhao and Jian Cheng and Tao Liu and Jiyang Jiang and Forrest Koch and Perminder S. Sachdev and Peter J. Basser and Wei Wen and for the Alzheimer's Disease Neuroimaging Initiative}, doi = {10.1002/hbm.25628}, journal = {Human Brain Mapping}, pdf = {https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/hbm.25628}, title = {Orientational changes of white matter fibers in Alzheimer's disease and amnestic mild cognitive impairment}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/hbm.25628}, year = {2021} }Abstract
Abstract White matter abnormalities represent early neuropathological events in neurodegenerative diseases such as Alzheimer's disease (AD), investigating these white matter alterations would likely provide valuable insights into pathological changes over the course of AD. Using a novel mathematical framework called “Director Field Analysis” (DFA), we investigated the geometric microstructural properties (i.e., splay, bend, twist, and total distortion) in the orientation of white matter fibers in AD, amnestic mild cognitive impairment (aMCI), and cognitively normal (CN) individuals from the Alzheimer's Disease Neuroimaging Initiative 2 database. Results revealed that AD patients had extensive orientational changes in the bilateral anterior thalamic radiation, corticospinal tract, inferior and superior longitudinal fasciculus, inferior fronto-occipital fasciculus, and uncinate fasciculus in comparison with CN. We postulate that these orientational changes of white matter fibers may be partially caused by the expansion of lateral ventricle, white matter atrophy, and gray matter atrophy in AD. In contrast, aMCI individuals showed subtle orientational changes in the left inferior longitudinal fasciculus and right uncinate fasciculus, which showed a significant association with the cognitive performance, suggesting that these regions may be preferential vulnerable to breakdown by neurodegenerative brain disorders, thereby resulting in the patients' cognitive impairment. To our knowledge, this article is the first to examine geometric microstructural changes in the orientation of white matter fibers in AD and aMCI. Our findings demonstrate that the orientational information of white matter fibers could provide novel insight into the underlying biological and pathological changes in AD and aMCI.
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Jian Cheng*, Dinggang Shen, Pew-Thian Yap*, Peter J. Basser*,
"Single- and Multiple-Shell Uniform Sampling Schemes for Diffusion MRI Using Spherical Codes",
IEEE Transactions on Medical Imaging (TMI), vol. 37, no. 1, pp. 185–199, 2018.
[bibtex]
[abstract]
[arxiv]
[project]
[citations: 38]
Bibtex
@article{cheng:TMI2017, author = {Jian Cheng and Dinggang Shen and Pew-Thian Yap and Peter J. Basser}, doi = {10.1109/TMI.2017.2756072}, journal = {IEEE Transactions on Medical Imaging}, number = {1}, pages = {185-199}, pdf = {https://arxiv.org/pdf/1706.06682.pdf}, publisher = {IEEE}, title = {Single- and Multiple-Shell Uniform Sampling Schemes for Diffusion MRI Using Spherical Codes}, url = {https://dx.doi.org/10.1109/TMI.2017.2756072}, volume = {37}, year = {2018} }Abstract
In diffusion MRI (dMRI), a good sampling scheme is important for efficient acquisition and robust reconstruction. Diffusion weighted signal is normally acquired on single or multiple shells in q-space. Signal samples are typically distributed uniformly on different shells to make them invariant to the orientation of structures within tissue, or the laboratory coordinate frame. The Electrostatic Energy Minimization (EEM) method, originally proposed for single shell sampling scheme in dMRI, was recently generalized to multi- shell schemes, called Generalized EEM (GEEM). GEEM has been successfully used in the Human Connectome Project (HCP). However, EEM does not directly address the goal of optimal sampling, i.e., achieving large angular separation between sampling points. In this paper, we propose a more natural formulation, called Spherical Code (SC), to directly maximize the minimal angle between different samples in single or multiple shells. We consider not only continuous problems to design single or multiple shell sampling schemes, but also discrete problems to uniformly extract sub-sampled schemes from an existing single or multiple shell scheme, and to order samples in an existing scheme. We propose five algorithms to solve the above problems, including an incremental SC (ISC), a sophisticated greedy algorithm called Iterative Maximum Overlap Construction (IMOC), an 1-Opt greedy method, a Mixed Integer Linear Programming (MILP) method, and a Constrained Non-Linear Optimization (CNLO) method. To our knowledge, this is the first work to use the SC formulation for single or multiple shell sampling schemes in dMRI. Experimental results indicate that SC methods obtain larger angular separation and better rotational invariance than the state- of-the-art EEM and GEEM. The related codes and a tutorial have been released in DMRITool.
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Jian Cheng*, Peter J. Basser*,
"Director Field Analysis (DFA): Exploring Local White Matter Geometric Structure in diffusion MRI",
Medical Image Analysis (MedIA), vol. 43, pp. 112–128, 2018.
[bibtex]
[abstract]
[arxiv]
[citations: 14]
Bibtex
@article{cheng:MedIA2017, author = {Jian Cheng and Peter J. Basser}, doi = {10.1016/j.media.2017.10.003}, journal = {Medical Image Analysis}, pages = {112-128}, pdf = {https://arxiv.org/pdf/1706.01862.pdf}, publisher = {Elsevier}, title = {Director Field Analysis (DFA): Exploring Local White Matter Geometric Structure in diffusion MRI}, url = {https://dx.doi.org/10.1016/j.media.2017.10.003}, volume = {43}, year = {2018} }Abstract
In Diffusion Tensor Imaging (DTI) or High Angular Resolution Diffusion Imaging (HARDI), a tensor field or a spherical function field (e.g., an orientation distribution function field), can be estimated from measured diffusion weighted images. In this paper, inspired by the microscopic theoretical treatment of phases in liquid crystals, we introduce a novel mathematical framework, called Director Field Analysis (DFA), to study local geometric structural information of white matter based on the reconstructed tensor field or spherical function field: 1) We propose a set of mathematical tools to process general director data, which consists of dyadic tensors that have orientations but no direction. 2) We propose Orientational Order (OO) and Orientational Dispersion (OD) indices to describe the degree of alignment and dispersion of a spherical function in a single voxel or in a region, respectively; 3) We also show how to construct a local orthogonal coordinate frame in each voxel exhibiting anisotropic diffusion; 4) Finally, we define three indices to describe three types of orientational distortion (splay, bend, and twist) in a local spatial neighborhood, and a total distortion index to describe distortions of all three types. To our knowledge, this is the first work to quantitatively describe orientational distortion (splay, bend, and twist) in general spherical function fields from DTI or HARDI data. The proposed DFA and its related mathematical tools can be used to process not only diffusion MRI data but also general director field data, and the proposed scalar indices are useful for detecting local geometric changes of white matter for voxel-based or tract-based analysis in both DTI and HARDI acquisitions. The related codes and a tutorial for DFA will be released in DMRITool.
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Hao Guan, Tao Liu*, Jiyang Jiang, Dacheng Tao, Jicong Zhang, Haijun Niu, Wanlin Zhu, Yilong Wang, Jian Cheng*, Nicole A. Kochan, Henry Brodaty, Perminder Sachdev, Wei Wen,
"Classifying MCI subtypes in community-dwelling elderly using cross-sectional and longitudinal MRI-based biomarkers",
Frontiers in Aging Neuroscience, vol. 9, pp. 309, 2017.
[bibtex]
[abstract]
[citations: 27]
Bibtex
@article{tao:cheng:FNAGI2017, author = {Hao Guan and Tao Liu and Jiyang Jiang and Dacheng Tao and Jicong Zhang and Haijun Niu and Wanlin Zhu and Yilong Wang and Jian Cheng and Nicole A. Kochan and Henry Brodaty and Perminder Sachdev and Wei Wen}, doi = {10.3389/fnagi.2017.00309}, journal = {Frontiers in Aging Neuroscience}, pages = {309}, pdf = {http://journal.frontiersin.org/article/10.3389/fnagi.2017.00309/pdf}, title = {Classifying MCI subtypes in community-dwelling elderly using cross-sectional and longitudinal MRI-based biomarkers}, url = {https://dx.doi.org/10.3389/fnagi.2017.00309}, volume = {9}, year = {2017} }Abstract
Amnestic MCI (aMCI) and non-amnestic MCI (naMCI) are considered to differ in etiology and outcome. Accurately classifying MCI into meaningful subtypes would enable early intervention with targeted treatment. In this study, we employed structural magnetic resonance imaging (MRI) for MCI subtype classification. This was carried out in a sample of 184 community-dwelling individuals (aged 73–85 years). Cortical surface based measurements were computed from longitudinal and cross-sectional scans. By introducing a feature selection algorithm, we identified a set of discriminative features, and further investigated the temporal patterns of these features. A voting classifier was trained and evaluated via 10 iterations of cross-validation. The best classification accuracies achieved were: 77% (naMCI vs. aMCI), 81% (aMCI vs. cognitively normal (CN)) and 70% (naMCI vs. CN). The best results for differentiating aMCI from naMCI were achieved with baseline features. Hippocampus, amygdala and frontal pole were found to be most discriminative for classifying MCI subtypes. Additionally, we observed the dynamics of classification of several MRI biomarkers. Learning the dynamics of atrophy may aid in the development of better biomarkers, as it may track the progression of cognitive impairment.
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Feng Shi#, Jian Cheng#, Li Wang, Pew-Thian Yap, Dinggang Shen*,
"LRTV: MR image super-resolution with low-rank and total variation regularizations",
IEEE Transactions on Medical Imaging (TMI), vol. 34, no. 12, pp. 2459–2466, 2015.
[bibtex]
[abstract]
[code]
[citations: 337]
(F. Shi and J. Cheng contributed equally.)
Bibtex
@article{shi_TMI2015, author = {Feng Shi and Jian Cheng and Li Wang and Pew-Thian Yap and Dinggang Shen}, doi = {10.1109/TMI.2015.2437894}, hal_id = {hal-01154770}, journal = {IEEE Transactions on Medical Imaging}, number = {12}, pages = {2459-2466}, pdf = {https://hal.archives-ouvertes.fr/hal-01154770/document}, publisher = {IEEE}, title = {LRTV: MR image super-resolution with low-rank and total variation regularizations}, url = {https://dx.doi.org/10.1109/TMI.2015.2437894}, volume = {34}, year = {2015} }Abstract
Image super-resolution (SR) aims to recover high-resolution images from their low-resolution counterparts for improving image analysis and visualization. Interpolation methods, widely used for this purpose, often result in images with blurred edges and blocking effects. More advanced methods such as total variation (TV) retain edge sharpness during image recovery. However, these methods only utilize information from local neighborhoods, neglecting useful information from remote voxels. In this paper, we propose a novel image SR method that integrates both local and global information for effective image recovery. This is achieved by, in addition to TV, low-rank regularization that enables utilization of information throughout the image. The optimization problem can be solved effectively via alternating direction method of multipliers (ADMM). Experiments on MR images of both adult and pediatric subjects demonstrate that the proposed method enhances the details in the recovered high-resolution images, and outperforms methods such as the nearest-neighbor interpolation, cubic interpolation, iterative back projection (IBP), non-local means (NLM), and TV-based up- sampling.
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Jian Cheng*, Rachid Deriche, Tianzi Jiang, Dinggang Shen, Pew-Thian Yap*,
"Non-Negative Spherical Deconvolution (NNSD) for estimation of fiber Orientation Distribution Function in single-/multi-shell diffusion MRI",
NeuroImage, vol. 101, pp. 750–764, 2014.
[bibtex]
[abstract]
[citations: 43]
(Honorable Mention in ISBI HARDI Reconstruction Challenge in 2013; the best technique in terms of local comparison.)
Bibtex
@article{cheng_NI2014, author = {Jian Cheng and Rachid Deriche and Tianzi Jiang and Dinggang Shen and Pew-Thian Yap}, doi = {10.1016/j.neuroimage.2014.07.062}, journal = {NeuroImage}, pages = {750-764}, pdf = {https://pdfs.semanticscholar.org/fc76/327ac26d573283db98939119660588c2af6f.pdf}, publisher = {Elsevier}, title = {Non-Negative Spherical Deconvolution (NNSD) for estimation of fiber Orientation Distribution Function in single-/multi-shell diffusion MRI}, url = {https://dx.doi.org/10.1016/j.neuroimage.2014.07.062}, volume = {101}, year = {2014} }Abstract
Spherical Deconvolution (SD) is commonly used for estimating fiber Orientation Distribution Functions (fODFs) from diffusion-weighted signals. Existing SD methods can be classified into two categories: 1) Continuous Representation based SD (CR-SD), where typically Spherical Harmonic (SH) representation is used for convenient analytical solutions, and 2) Discrete Representation based SD (DR- SD), where the signal profile is represented by a discrete set of basis functions uniformly oriented on the unit sphere. A feasible fODF should be non-negative and should integrate to unity throughout the unit sphere S 2. However, to our knowledge, most existing SH- based SD methods enforce non-negativity only on discretized points and not the whole continuum of S 2. Maximum Entropy SD (MESD) and Cartesian Tensor Fiber Orientation Distributions (CT-FOD) are the only SD methods that ensure non-negativity throughout the unit sphere. They are however computational intensive and are susceptible to errors caused by numerical spherical integration. Existing SD methods are also known to overestimate the number of fiber directions, especially in regions with low anisotropy. DR-SD introduces additional error in peak detection owing to the angular discretization of the unit sphere. This paper proposes a SD framework, called Non-Negative SD (NNSD), to overcome all the limitations above. NNSD is significantly less susceptible to the false-positive peaks, uses SH representation for efficient analytical spherical deconvolution, and allows accurate peak detection throughout the whole unit sphere. We further show that NNSD and most existing SD methods can be extended to work on multi- shell data by introducing a three-dimensional fiber response function. We evaluated NNSD in comparison with Constrained SD (CSD), a quadratic programming variant of CSD, MESD, and an L1-norm regularized non-negative least-squares DR-SD. Experiments on synthetic and real single-/multi-shell data indicate that NNSD improves estimation performance in terms of mean difference of angles, peak detection consistency, and anisotropy contrast between isotropic and anisotropic regions.
Conference Articles¶
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Si-Miao Zhang, Jing Wang, Yi-Xuan Wang, Tao Liu, Haogang Zhu, Han Zhang, Jian Cheng*,
"Mixed Integer Linear Programming for Discrete Sampling Scheme Design in Diffusion MRI",
International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI'24), pp. 313–322, 2024.
[bibtex]
Bibtex
@inproceedings{zhang:MICCAI2024mixed, author = {Si-Miao Zhang and Jing Wang and Yi-Xuan Wang and Tao Liu and Haogang Zhu and Han Zhang and Jian Cheng}, booktitle = {International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI'24)}, doi = {10.1007/978-3-031-72069-7_30}, organization = {Springer}, pages = {313-322}, title = {Mixed Integer Linear Programming for Discrete Sampling Scheme Design in Diffusion MRI}, url = {https://dx.doi.org/10.1007/978-3-031-72069-7_30}, year = {2024} } -
Jing Yang, Jian Cheng*, Cheng Li, Wenxin Fan, Juan Zou, Ruoyou Wu, Shanshan Wang*,
"Simultaneous q-Space Sampling Optimization and Reconstruction for Fast and High-fidelity Diffusion Magnetic Resonance Imaging",
IEEE International Symposium on Biomedical Imaging: From Nano to Macro (ISBI'24), 2024.
[bibtex]
[abstract]
[arxiv]
[citations: 1]
Bibtex
@inproceedings{yang2024simultaneous, author = {Jing Yang and Jian Cheng and Cheng Li and Wenxin Fan and Juan Zou and Ruoyou Wu and Shanshan Wang}, booktitle = {IEEE International Symposium on Biomedical Imaging: From Nano to Macro (ISBI'24)}, pdf = {https://arxiv.org/pdf/2401.01662.pdf}, title = {Simultaneous q-Space Sampling Optimization and Reconstruction for Fast and High-fidelity Diffusion Magnetic Resonance Imaging}, url = {https://arxiv.org/abs/2401.01662}, year = {2024} }Abstract
Diffusion Magnetic Resonance Imaging (dMRI) plays a crucial role in the noninvasive investigation of tissue microstructural properties and structural connectivity in the in vivo human brain. However, to effectively capture the intricate characteristics of water diffusion at various directions and scales, it is important to employ comprehensive q-space sampling. Unfortunately, this requirement leads to long scan times, limiting the clinical applicability of dMRI. To address this challenge, we propose SSOR, a Simultaneous q-Space sampling Optimization and Reconstruction framework. We jointly optimize a subset of q-space samples using a continuous representation of spherical harmonic functions and a reconstruction network. Additionally, we integrate the unique properties of diffusion magnetic resonance imaging (dMRI) in both the q-space and image domains by applying l1-norm and total-variation regularization.The experiments conducted on HCP data demonstrate that SSOR has promising strengths both quantitatively and qualitatively and exhibits robustness to noise
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Ziyang Liu#, Jian Cheng#, Haogang Zhu, Jicong Zhang, Tao Liu,
"Brain Age Estimation from MRI Using a Two-Stage Cascade Network with Ranking Loss",
International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI'20), pp. 198–207, 2020.
[bibtex]
[abstract]
[code]
[citations: 7]
(Ziyang Liu and Jian Cheng contributed equally.)
Bibtex
@inproceedings{liu:MICCAI2020, author = {Ziyang Liu and Jian Cheng and Haogang Zhu and Jicong Zhang and Tao Liu}, booktitle = {International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI'20)}, doi = {10.1007/978-3-030-59728-3_20}, organization = {Springer}, pages = {198-207}, title = {Brain Age Estimation from MRI Using a Two-Stage Cascade Network with Ranking Loss}, url = {https://dx.doi.org/10.1007/978-3-030-59728-3_20}, year = {2020} }Abstract
As age increases, human brains will be aged, and people tend to experience cognitive decline with a higher risk of neuro- degenerative disease and dementia. Recently, it was reported that deep neural networks, e.g., 3D convolutional neural networks (CNN), are able to predict chronological age accurately in healthy people from their T1-weighted magnetic resonance images (MRI). The predicted age, called as “brain age” or “brain predicted age”, could be a biomarker of the brain ageing process. In this paper, we propose a novel 3D convolutional network, called as two-stage-age- net (TSAN), for brain age estimation from T1-weighted MRI data. Compared with the state-of-the-art CNN by Cole et al., TSAN has several improvements: 1) TSAN uses a two-stage cascade architecture, where the first network is to estimate a discretized age range, then the second network is to further estimate the brain age more accurately; 2) Besides using the traditional mean square error (MSE) loss between chronological and estimated ages, TSAN considers two additional novel ranking losses, based on paired samples and a batch of samples, for regularizing the training process; 3) TSAN uses densely connected paths to combine feature maps with different scales; 4) TSAN considers gender labels as input features for the network, considering brains of male and female age differently. The proposed TSAN was validated in three public datasets. The experiments showed that TSAN could provide accurate brain age estimation in healthy subjects, yielding a mean absolute error (MAE) of 2.428, and a Pearson’s correlation coefficient (PCC) of 0.985, between the estimated and the chronological ages.
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Jian Cheng, Tao Liu, Feng Shi, Ruiliang Bai, Jicong Zhang, Haogang Zhu, Dacheng Tao, Peter J Basser,
"On Quantifying Local Geometric Structures of Fiber Tracts",
Medical Image Computing and Computer-Assisted Intervention (MICCAI'18), pp. 392–400, 2018.
[bibtex]
[abstract]
[citations: 2]
Bibtex
@inproceedings{cheng:MICCAI2018, author = {Jian Cheng and Tao Liu and Feng Shi and Ruiliang Bai and Jicong Zhang and Haogang Zhu and Dacheng Tao and Peter J Basser}, booktitle = {Medical Image Computing and Computer-Assisted Intervention (MICCAI'18)}, doi = {10.1007/978-3-030-00931-1_45}, hal_id = {hal-02098668}, organization = {Springer}, pages = {392-400}, pdf = {https://hal.archives-ouvertes.fr/hal-02098668/document}, title = {On Quantifying Local Geometric Structures of Fiber Tracts}, url = {https://dx.doi.org/10.1007/978-3-030-00931-1_45}, year = {2018} }Abstract
In diffusion MRI, fiber tracts, represented by densely distributed 3D curves, can be estimated from diffusion weighted images using tractography. The spatial geometric structure of white matter fiber tracts is known to be complex in human brain, but it carries intrinsic information of human brain. In this paper, inspired by studies of liquid crystals, we propose tract-based director field analysis (tDFA) with total six rotationally invariant scalar indices to quantify local geometric structures of fiber tracts. The contributions of tDFA include: (1) We propose orientational order (OO) and orientational dispersion (OD) indices to quantify the degree of alignment and dispersion of fiber tracts; (2) We define the local orthogonal frame for a set of unoriented curves, which is proved to be a generalization of the Frenet frame defined for a single oriented curve; (3) With the local orthogonal frame, we propose splay, bend, and twist indices to quantify three types of orientational distortion of local fiber tracts, and a total distortion index to describe distortions of all three types. The proposed tDFA for fiber tracts is a generalization of the voxel- based DFA (vDFA) which was recently proposed for a spherical function field (i.e., an ODF field). To our knowledge, this is the first work to quantify orientational distortion (splay, bend, twist, and total distortion) of fiber tracts. Experiments show that the proposed scalar indices are useful descriptors of local geometric structures to visualize and analyze fiber tracts.
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Jian Cheng, Peter J. Basser,
"Director Field Analysis to Explore Local White Matter Geometric Structure in diffusion MRI",
International Conference on Information Processing in Medical Imaging (IPMI'17), vol. 10265, pp. 427–439, 2017.
[bibtex]
[abstract]
(Oral presentation; Turned to be a poster due to conflicting travel plans.)
Bibtex
@inproceedings{cheng:IPMI2017, author = {Jian Cheng and Peter J. Basser}, booktitle = {International Conference on Information Processing in Medical Imaging (IPMI'17)}, doi = {10.1007/978-3-319-59050-9_34}, hal_id = {hal-01511573}, pages = {427-439}, pdf = {https://hal.archives-ouvertes.fr/hal-01511573/document}, title = {Director Field Analysis to Explore Local White Matter Geometric Structure in diffusion MRI}, url = {https://dx.doi.org/10.1007/978-3-319-59050-9_34}, volume = {10265}, year = {2017} }Abstract
In diffusion MRI, a tensor field or a spherical function field, e.g., an Orientation Distribution Function (ODF) field, are estimated from measured diffusion weighted images. In this paper, inspired by microscopic theoretical treatment of phases in liquid crystals, we introduce a novel mathematical framework, called Director Field Analysis (DFA), to study local geometric structural information of white matter from the estimated tensor field or spherical function field. 1) We propose Orientational Order (OO) and Orientational Dispersion (OD) indices to describe the degree of alignment and dispersion of a spherical function in each voxel; 2) We estimate a local orthogonal coordinate frame in each voxel with anisotropic diffusion; 3) Finally, we define three indices to describe three types of orientational distortion (splay, bend, and twist) in a local spatial neighborhood, and a total distortion index to describe distortions of all three types. To our knowledge, this is the first work to \emph{quantitatively} describe orientational distortion (splay, bend, and twist) in diffusion MRI. The proposed scalar indices are useful to detect local geometric changes of white matter for voxel-based or tract-based analysis in both DTI and HARDI acquisitions. -
Jian Cheng, Dinggang Shen, Pew-Thian Yap, Peter J. Basser,
"Tensorial Spherical Polar Fourier diffusion MRI with Optimal Dictionary Learning",
International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI'15), vol. 9349, pp. 174–182, 2015.
[bibtex]
[abstract]
[project]
[citations: 13]
Bibtex
@inproceedings{cheng_MICCAI2015, author = {Jian Cheng and Dinggang Shen and Pew-Thian Yap and Peter J. Basser}, booktitle = {International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI'15)}, doi = {10.1007/978-3-319-24553-9_22}, organization = {Springer}, pages = {174-182}, pdf = {https://hal.archives-ouvertes.fr/hal-01164809/document}, series = {LNCS}, title = {Tensorial Spherical Polar Fourier diffusion MRI with Optimal Dictionary Learning}, url = {https://dx.doi.org/10.1007/978-3-319-24553-9_22}, volume = {9349}, year = {2015} }Abstract
High Angular Resolution Diffusion Imaging (HARDI) can characterize complex white matter micro-structure, avoiding the Gaussian diffusion assumption inherent in Diffusion Tensor Imaging (DTI). However, HARDI methods normally require significantly more signal measurements and a longer scan time than DTI, which limits its clinical utility. By considering sparsity of the diffusion signal, Compressed Sensing (CS) allows robust signal reconstruction from relatively fewer samples, reducing the scanning time. A good dictionary that sparsifies the signal is crucial for CS reconstruction. In this paper, we propose a novel method called Tensorial Spherical Polar Fourier Imaging (TSPFI) to recover continuous diffusion signal and diffusion propagator by representing the diffusion signal using an orthonormal TSPF basis. TSPFI is a generalization of the existing model-based method DTI and the model- free method SPFI. We also propose dictionary learning TSPFI (DL- TSPFI) to learn an even sparser dictionary represented as a linear combination of TSPF basis from continuous mixture of Gaussian signals. The learning process is efficiently performed in a small subspace of SPF coefficients, and the learned dictionary is proved to be sparse for all mixture of Gaussian signals by adaptively setting the tensor in TSPF basis. Then the learned DL-TSPF dictionary is optimally and adaptively applied to different voxels using DTI and a weighted LASSO for CS reconstruction. DL-TSPFI is a generalization of DL-SPFI, by considering general adaptive tensor setting instead of a scale value. The experiments demonstrated that the learned DL-TSPF dictionary has a sparser representation and lower reconstruction Root-Mean-Squared-Error (RMSE) than both the original SPF basis and the DL-SPF dictionary.
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Jian Cheng, Dinggang Shen, Pew-Thian Yap, Peter J. Basser,
"Novel single and multiple shell uniform sampling schemes for diffusion MRI using spherical codes",
International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI'15), vol. 9349, pp. 28–36, 2015.
[bibtex]
[abstract]
[project]
[citations: 9]
(early accepted)
Bibtex
@inproceedings{cheng_MICCAI2015_sampling, author = {Jian Cheng and Dinggang Shen and Pew-Thian Yap and Peter J. Basser}, booktitle = {International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI'15)}, doi = {10.1007/978-3-319-24553-9_4}, organization = {Springer}, pages = {28-36}, pdf = {https://hal.archives-ouvertes.fr/hal-01154774/document}, title = {Novel single and multiple shell uniform sampling schemes for diffusion MRI using spherical codes}, url = {https://dx.doi.org/10.1007/978-3-319-24553-9_4}, volume = {9349}, year = {2015} }Abstract
A good data sampling scheme is important for diffusion MRI acquisition and reconstruction. Diffusion Weighted Imaging (DWI) data is normally acquired on single or multiple shells in q-space. The samples in different shells are typically distributed uniformly, because they should be invariant to the orientation of structures within tissue, or the laboratory coordinate frame. The Electrostatic Energy Minimization (EEM) method, originally proposed for single shell sampling scheme in dMRI by Jones et al., was recently generalized to the multi-shell case, called generalized EEM (GEEM). GEEM has been successfully used in the Human Connectome Project (HCP). Recently, the Spherical Code (SC) concept was proposed to maximize the minimal angle between different samples in single or multiple shells, producing a larger angular separation and better rotational invariance than the GEEM method. In this paper, we propose two novel algorithms based on the SC concept: 1) an efficient incremental constructive method, called Iterative Maximum Overlap Construction (IMOC), to generate a sampling scheme on a discretized sphere; 2) a constrained non-linear optimization (CNLO) method to update a given initial scheme on the continuous sphere. Compared to existing incremental estimation methods, IMOC obtains schemes with much larger separation angles between samples, which are very close to the best known solutions in single shell case. Compared to the existing Riemannian gradient descent method, CNLO is more robust and stable. Experiments demonstrated that the two proposed methods provide larger separation angles and better rotational invariance than the state-of-the-art GEEM and methods based on the SC concept.
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Jian Cheng, Dinggang Shen, Peter J. Basser, Pew-Thian Yap,
"Joint 6D k-q Space Compressed Sensing for Accelerated High Angular Resolution Diffusion MRI",
International Conference on Information Processing in Medical Imaging (IPMI'15), vol. 9123, pp. 782–793, 2015.
[bibtex]
[abstract]
[citations: 32]
Bibtex
@inproceedings{cheng_IPMI2015, author = {Jian Cheng and Dinggang Shen and Peter J. Basser and Pew-Thian Yap}, booktitle = {International Conference on Information Processing in Medical Imaging (IPMI'15)}, doi = {10.1007/978-3-319-19992-4_62}, organization = {Springer}, pages = {782-793}, pdf = {https://hal.archives-ouvertes.fr/hal-01356133/document}, title = {Joint 6D k-q Space Compressed Sensing for Accelerated High Angular Resolution Diffusion MRI}, url = {https://dx.doi.org/10.1007/978-3-319-19992-4_62}, volume = {9123}, year = {2015} }Abstract
High Angular Resolution Diffusion Imaging (HARDI) avoids the Gaussian diffusion assumption that is inherent in Diffusion Tensor Imaging (DTI), and is capable of characterizing complex white matter micro-structure with greater precision. However, HARDI methods such as Diffusion Spectrum Imaging (DSI) typically require significantly more signal measurements than DTI, resulting in prohibitively long scanning times. One of the goals in HARDI research is therefore to improve estimation of quantities such as the Ensemble Average Propagator (EAP) and the Orientation Distribution Function (ODF) with a limited number of diffusion-weighted measurements. A popular approach to this problem, Compressed Sensing (CS), affords highly accurate signal reconstruction using significantly fewer (sub- Nyquist) data points than required traditionally. Existing approaches to CS diffusion MRI (CS-dMRI) mainly focus on applying CS in the q-space of diffusion signal measurements and fail to take into consideration information redundancy in the k-space. In this paper, we propose a framework, called 6-Dimensional Compressed Sensing diffusion MRI (6D-CS-dMRI), for reconstruction of the diffusion signal and the EAP from data sub-sampled in both 3D k-space and 3D q-space. To our knowledge, 6D-CS-dMRI is the first work that applies compressed sensing in the full 6D k-q space and reconstructs the diffusion signal in the full continuous q-space and the EAP in continuous displacement space. Experimental results on synthetic and real data demonstrate that, compared with full DSI sampling in k-q space, 6D-CS-dMRI yields excellent diffusion signal and EAP reconstruction with low root-mean-square error (RMSE) using 11 times less samples (3-fold reduction in k-space and 3.7-fold reduction in q-space).
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Jian Cheng, Dinggang Shen, Pew-Thian Yap,
"Designing single- and multiple-shell sampling schemes for diffusion MRI using spherical code",
Medical Image Computing and Computer-Assisted Intervention (MICCAI'14), vol. 8675, pp. 281–288, 2014.
[bibtex]
[abstract]
[project]
[citations: 23]
(early accepted)
Bibtex
@inproceedings{cheng_MICCAI2014, author = {Jian Cheng and Dinggang Shen and Pew-Thian Yap}, booktitle = {Medical Image Computing and Computer-Assisted Intervention (MICCAI'14)}, doi = {10.1007/978-3-319-10443-0_36}, hal_id = {hal-01011897}, pages = {281-288}, pdf = {https://hal.archives-ouvertes.fr/hal-01011897/document}, publisher = {Springer}, title = {Designing single- and multiple-shell sampling schemes for diffusion MRI using spherical code}, url = {https://dx.doi.org/10.1007/978-3-319-10443-0_36}, volume = {8675}, year = {2014} }Abstract
In diffusion MRI (dMRI), determining an appropriate sampling scheme is crucial for acquiring the maximal amount of information for data reconstruction and analysis using the minimal amount of time. For single-shell acquisition, uniform sampling without directional preference is usually favored. To achieve this, a commonly used approach is the Electrostatic Energy Minimization (EEM) method introduced in dMRI by Jones et al. However, the electrostatic energy formulation in EEM is not directly related to the goal of optimal sampling-scheme design, i.e., achieving large angular separation between sampling points. A mathematically more natural approach is to consider the Spherical Code (SC) formulation, which aims to achieve uniform sampling by maximizing the minimal angular difference between sampling points on the unit sphere. Although SC is well studied in the mathematical literature, its current formulation is limited to a single shell and is not applicable to multiple shells. Moreover, SC, or more precisely continuous SC (CSC), currently can only be applied on the continuous unit sphere and hence cannot be used in situations where one or several subsets of sampling points need to be determined from an existing sampling scheme. In this case, discrete SC (DSC) is required. In this paper, we propose novel DSC and CSC methods for designing uniform single-/multi-shell sampling schemes. The DSC and CSC formulations are solved respectively by Mixed Integer Linear Programming (MILP) and a gradient descent approach. A fast greedy incremental solution is also provided for both DSC and CSC. To our knowledge, this is the first work to use SC formulation for designing sampling schemes in dMRI. Experimental results indicate that our methods obtain larger angular separation and better rotational invariance than the generalized EEM (gEEM) method currently used in the Human Connectome Project (HCP).
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Feng Shi#, Jian Cheng#, Li Wang, Pew-Thian Yap, Dinggang Shen,
"Longitudinal guided super-resolution reconstruction of neonatal brain MR images",
MICCAI Workshop on Spatio-temporal Image Analysis for Longitudinal and Time-Series Image Data, vol. 8682, pp. 67–76, 2014.
[bibtex]
[abstract]
[citations: 7]
(F. Shi and J. Cheng contributed equally.)
Bibtex
@inproceedings{shi:2014, author = {Feng Shi and Jian Cheng and Li Wang and Pew-Thian Yap and Dinggang Shen}, booktitle = {MICCAI Workshop on Spatio-temporal Image Analysis for Longitudinal and Time-Series Image Data}, doi = {10.1007/978-3-319-14905-9_6}, organization = {Springer}, pages = {67-76}, pdf = {https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4669195/pdf/nihms691856.pdf}, title = {Longitudinal guided super-resolution reconstruction of neonatal brain MR images}, url = {https://dx.doi.org/10.1007/978-3-319-14905-9_6}, volume = {8682}, year = {2014} }Abstract
Neonatal images have low spatial resolution and insufficient tissue contrast. Generally, interpolation methods are used to upsample neonatal images to a higher resolution for more effective image analysis. However, the resulting images are often blurry and are susceptible to partial volume effect. In this paper, we propose an algorithm that utilizes longitudinal prior information for effective super-resolution reconstruction of neonatal images. We use a non- local approach to learn the spatial relationships of brain structures in high-resolution longitudinal images and apply this information to the super-resolution reconstruction of the neonatal image. In other words, the recurring patterns throughout the longitudinal scans are leveraged for reconstructing the neonatal image with high resolution. To solve this otherwise ill-posed inverse problem, low-rank and total-variation regularizations are enforced. Experiments performed on both T1- and T2-weighted MR images of 28 neonates demonstrate that the proposed method is capable of recovering more structural details and outperforms methods such as nearest neighbor interpolation, spline-based interpolation, non-local means upsampling, and both low-rank and total variation based super-resolution
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Jian Cheng, Tianzi Jiang, Rachid Deriche, Dinggang Shen, Pew-Thian Yap,
"Regularized Spherical Polar Fourier Diffusion MRI with Optimal Dictionary Learning",
The 16th International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI'13), vol. 8149, pp. 639–646, 2013.
[bibtex]
[abstract]
[project]
[citations: 16]
Bibtex
@inproceedings{cheng_DL-SPFI_MICCAI13, author = {Jian Cheng and Tianzi Jiang and Rachid Deriche and Dinggang Shen and Pew-Thian Yap}, booktitle = {The 16th International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI'13)}, doi = {10.1007/978-3-642-40811-3_80}, hal_id = {hal-00824507}, pages = {639-646}, pdf = {https://hal.inria.fr/hal-00824507/document}, title = {Regularized Spherical Polar Fourier Diffusion MRI with Optimal Dictionary Learning}, url = {https://dx.doi.org/10.1007/978-3-642-40811-3_80}, volume = {8149}, year = {2013} }Abstract
Compressed Sensing (CS) takes advantage of signal sparsity or compressibility and allows superb signal reconstruction from relatively few measurements. Based on CS theory, a suitable dictionary for sparse representation of the signal is required. In diffusion MRI (dMRI), CS methods proposed for reconstruction of diffusion-weighted signal and the Ensemble Average Propagator (EAP) utilize two kinds of Dictionary Learning (DL) methods: 1) Discrete Representation DL (DR-DL), and 2) Continuous Representation DL (CR- DL). DR-DL is susceptible to numerical inaccuracy owing to interpolation and regridding errors in a discretized q-space. In this paper, we propose a novel CR-DL approach, called Dictionary Learning - Spherical Polar Fourier Imaging (DL-SPFI) for effective compressed-sensing reconstruction of the q-space diffusion-weighted signal and the EAP. In DL-SPFI, a dictionary that sparsifies the signal is learned from the space of continuous Gaussian diffusion signals. The learned dictionary is then adaptively applied to different voxels using a weighted LASSO framework for robust signal reconstruction. Compared with the start-of-the-art CR-DL and DR-DL methods proposed by Merlet et al. and Bilgic et al., respectively, our work offers the following advantages. First, the learned dictionary is proved to be optimal for Gaussian diffusion signals. Second, to our knowledge, this is the first work to learn a voxel- adaptive dictionary. The importance of the adaptive dictionary in EAP reconstruction will be demonstrated theoretically and empirically. Third, optimization in DL-SPFI is only performed in a small subspace resided by the SPF coefficients, as opposed to the q-space approach utilized by Merlet et al. We experimentally evaluated DL-SPFI with respect to L1-norm regularized SPFI (L1-SPFI), which uses the original SPF basis, and the DR-DL method proposed by Bilgic et al. The experiment results on synthetic and real data indicate that the learned dictionary produces sparser coefficients than the original SPF basis and results in significantly lower reconstruction error than Bilgic et al.'s method.
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Feng Shi#, Jian Cheng#, Li Wang, Pew-Thian Yap, Dinggang Shen,
"Low-Rank Total Variation for Image Super-Resolution",
Medical Image Computing and Computer-Assisted Intervention (MICCAI'13), vol. 8149, pp. 155–162, 2013.
[bibtex]
[abstract]
[code]
[citations: 54]
(F. Shi and J. Cheng contributed equally.)
Bibtex
@inproceedings{shi_MICCAI13, author = {Feng Shi and Jian Cheng and Li Wang and Pew-Thian Yap and Dinggang Shen}, booktitle = {Medical Image Computing and Computer-Assisted Intervention (MICCAI'13)}, doi = {10.1007/978-3-642-40811-3_20}, pages = {155-162}, pdf = {https://www.researchgate.net/profile/Jian_Cheng2/publication/260127836_Low-Rank_Total_Variation_for_Image_Super-Resolution/links/0a85e52f69f43abff6000000.pdf}, publisher = {Springer}, title = {Low-Rank Total Variation for Image Super-Resolution}, url = {https://dx.doi.org/10.1007/978-3-642-40811-3_20}, volume = {8149}, year = {2013} }Abstract
Most natural images can be approximated using their low-rank components. This fact has been successfully exploited in recent advancements of matrix completion algorithms for image recovery. However, a major limitation of low-rank matrix completion algorithms is that they cannot recover the case where a whole row or column is missing. The missing row or column will be simply filled as an arbitrary combination of other rows or columns with known values. This precludes the application of matrix completion to problems such as super-resolution (SR) where missing values in many rows and columns need to be recovered in the process of up-sampling a low- resolution image. Moreover, low-rank regularization considers information globally from the whole image and does not take proper consideration of local spatial consistency. Accordingly, we propose in this paper a solution to the SR problem via simultaneous (global) low-rank and (local) total variation (TV) regularization. We solve the respective cost function using the alternating direction method of multipliers (ADMM). Experiments on MR images of adults and pediatric subjects demonstrate that the proposed method enhances the details of the recovered high-resolution images, and outperforms the nearest-neighbor interpolation, cubic interpolation, non-local means, and TV-based up-sampling.
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Jian Cheng, Rachid Deriche, Tianzi Jiang, Dinggang Shen, Pew-Thian Yap,
"Non-Negative Spherical Deconvolution (NNSD) for Fiber Orientation Distribution Function Estimation",
MICCAI Workshop on Computational Diffusion MRI (CDMRI'13), pp. 81–93, 2013.
[bibtex]
[abstract]
[citations: 4]
(Oral presentation)
Bibtex
@inproceedings{cheng_NNSD_CDMRI2013, author = {Jian Cheng and Rachid Deriche and Tianzi Jiang and Dinggang Shen and Pew-Thian Yap}, booktitle = {MICCAI Workshop on Computational Diffusion MRI (CDMRI'13)}, doi = {10.1007/978-3-319-02475-2_8}, hal_id = {hal-00967829}, pages = {81-93}, pdf = {https://hal.archives-ouvertes.fr/hal-00967829/document}, title = {Non-Negative Spherical Deconvolution (NNSD) for Fiber Orientation Distribution Function Estimation}, url = {https://dx.doi.org/10.1007/978-3-319-02475-2_8}, year = {2013} }Abstract
In diffusion Magnetic Resonance Imaging (dMRI), Spherical Deconvolution (SD) is a commonly used approach for estimating the fiber Orientation Distribution Function (fODF). As a Probability Density Function (PDF) that characterizes the distribution of fiber orientations, the fODF is expected to be non-negative and to integrate to unity on the continuous unit sphere $\mathbb{S}^2$. However, many existing approaches, despite using continuous representation such as Spherical Harmonics (SH), impose non- negativity only on discretized points of $\mathbb{S}^2$. Therefore, non-negativity is not guaranteed on the whole $\mathbb{S}^2$. Existing approaches are also known to exhibit false positive fODF peaks, especially in regions with low anisotropy, causing an over- estimation of the number of fascicles that traverse each voxel. This paper proposes a novel approach, called Non-Negative SD (NNSD), to overcome the above limitations. NNSD offers the following advantages. First, NNSD is the first SH based method that guarantees non-negativity of the fODF throughout the unit sphere. Second, unlike approaches such as Maximum Entropy SD (MESD), Cartesian Tensor Fiber Orientation Distribution (CT-FOD), and discrete representation based SD (DR-SD) techniques, the SH representation allows closed form of spherical integration, efficient computation in a low dimensional space resided by the SH coefficients, and accurate peak detection on the continuous domain defined by the unit sphere. Third, NNSD is significantly less susceptible to producing false positive peaks in regions with low anisotropy. Evaluations of NNSD in comparison with Constrained SD (CSD), MESD, and DR-SD (implemented using L1-regularized least-squares with non-negative constraint), indicate that NNSD yields improved performance for both synthetic and real data. The performance gain is especially prominent for high resolution (1.25 mm)^3 data. -
Jian Cheng, Tianzi Jiang, Rachid Deriche,
"Nonnegative Definite EAP and ODF Estimation via a Unified Multi-Shell HARDI Reconstruction",
Medical Image Computing and Computer-Assisted Intervention (MICCAI'12), vol. 6892, pp. 98–106, 2012.
[bibtex]
[abstract]
[citations: 15]
(MICCAI Student Travel Award)
Bibtex
@inproceedings{cheng_MICCAI2012, author = {Jian Cheng and Tianzi Jiang and Rachid Deriche}, booktitle = {Medical Image Computing and Computer-Assisted Intervention (MICCAI'12)}, doi = {10.1007/978-3-642-33418-4_39}, pages = {98-106}, pdf = {https://hal.archives-ouvertes.fr/hal-00759014/document}, publisher = {Springer Berlin / Heidelberg}, series = {LNCS}, title = {Nonnegative Definite EAP and ODF Estimation via a Unified Multi-Shell HARDI Reconstruction}, url = {https://dx.doi.org/10.1007/978-3-642-33418-4_39}, volume = {6892}, year = {2012} }Abstract
In High Angular Resolution Diffusion Imaging (HARDI), Orientation Distribution Function (ODF) and Ensemble Average Propagator (EAP) are two important Probability Density Functions (PDFs) which reflect the water diffusion and fiber orientations. Spherical Polar Fourier Imaging (SPFI) is a recent model-free multi-shell HARDI method which estimates both EAP and ODF from the diffusion signals with multiple b values. As physical PDFs, ODFs and EAPs are nonnegative definite respectively in their domains $\mathbb{S}^2$ and $\mathbb{R}^3$. However, existing ODF/EAP estimation methods like SPFI seldom consider this natural constraint. Although some works considered the nonnegative constraint on the given discrete samples of ODF/EAP, the estimated ODF/EAP is not guaranteed to be nonnegative definite in the whole continuous domain. The Riemannian framework for ODFs and EAPs has been proposed via the square root parameterization based on pre-estimated ODFs and EAPs by other methods like SPFI. However, there is no work on how to estimate the square root of ODF/EAP called as the wavefuntion directly from diffusion signals. In this paper, based on the Riemannian framework for ODFs/EAPs and Spherical Polar Fourier (SPF) basis representation, we propose a unified model-free multi-shell HARDI method, named as Square Root Parameterized Estimation (SRPE), to simultaneously estimate both the wavefunction of EAPs and the nonnegative definite ODFs and EAPs from diffusion signals. The experiments on synthetic data and real data showed SRPE is more robust to noise and has better EAP reconstruction than SPFI, especially for EAP profiles at large radius. -
Jian Cheng, Aurobrata Ghosh, Tianzi Jiang, Rachid Deriche,
"Diffeomorphism Invariant Riemannian Framework for Ensemble Average Propagator Computing",
Medical Image Computing and Computer-Assisted Intervention (MICCAI'11), vol. 6892, pp. 98–106, 2011.
[bibtex]
[abstract]
[citations: 7]
(MICCAI Student Travel Award)
Bibtex
@inproceedings{cheng_MICCAI2011, author = {Jian Cheng and Aurobrata Ghosh and Tianzi Jiang and Rachid Deriche}, booktitle = {Medical Image Computing and Computer-Assisted Intervention (MICCAI'11)}, doi = {10.1007/978-3-642-23629-7_13}, hal_id = {inria-00615431}, pages = {98-106}, pdf = {https://hal.inria.fr/inria-00615431/document}, publisher = {Springer Berlin / Heidelberg}, series = {LNCS}, title = {Diffeomorphism Invariant Riemannian Framework for Ensemble Average Propagator Computing}, url = {https://dx.doi.org/10.1007/978-3-642-23629-7_13}, volume = {6892}, year = {2011} }Abstract
Background: In Diffusion Tensor Imaging (DTI), Riemannian framework based on Information Geometry theory has been proposed for processing tensors on estimation, interpolation, smoothing, regularization, segmentation, statistical test and so on. Recently Riemannian framework has been generalized to Orientation Distribution Function (ODF) and it is applicable to any Probability Density Function (PDF) under orthonormal basis representation. Spherical Polar Fourier Imaging (SPFI) was proposed for ODF and Ensemble Average Propagator (EAP) estimation from arbitrary sampled signals without any assumption. Purpose: Tensors only can represent Gaussian EAP and ODF is the radial integration of EAP, while EAP has full information for diffusion process. To our knowledge, so far there is no work on how to process EAP data. In this paper, we present a Riemannian framework as a mathematical tool for such task. Method: We propose a state-of-the-art Riemannian framework for EAPs by representing the square root of EAP, called wavefunction based on quantum mechanics, with the Fourier dual Spherical Polar Fourier (dSPF) basis. In this framework, the exponential map, logarithmic map and geodesic have closed forms, and weighted Riemannian mean and median uniquely exist. We analyze theoretically the similarities and differences between Riemannian frameworks for EAPs and for ODFs and tensors. The Riemannian metric for EAPs is diffeomorphism invariant, which is the natural extension of the affine-invariant metric for tensors. We propose Log-Euclidean framework to fast process EAPs, and Geodesic Anisotropy (GA) to measure the anisotropy of EAPs. With this framework, many important data processing operations, such as interpolation, smoothing, atlas estimation, Principal Geodesic Analysis (PGA), can be performed on EAP data. Results and Conclusions: The proposed Riemannian framework was validated in synthetic data for interpolation, smoothing, PGA and in real data for GA and atlas estimation. Riemannian median is much robust for atlas estimation.
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Jian Cheng, Tianzi Jiang, Rachid Deriche,
"Theoretical Analysis and Practical Insights on EAP Estimation via a Unified HARDI Framework",
MICCAI Workshop on Computational Diffusion MRI (CDMRI'11), 2011.
[bibtex]
[abstract]
[project]
[citations: 24]
(Oral presentation)
Bibtex
@inproceedings{cheng_AFTSC_CDMRI2011, author = {Jian Cheng and Tianzi Jiang and Rachid Deriche}, booktitle = {MICCAI Workshop on Computational Diffusion MRI (CDMRI'11)}, hal_id = {inria-00615430}, pdf = {https://hal.inria.fr/inria-00615430/document}, title = {Theoretical Analysis and Practical Insights on EAP Estimation via a Unified HARDI Framework}, url = {https://hal.archives-ouvertes.fr/inria-00615430}, year = {2011} }Abstract
Since Diffusion Tensor Imaging (DTI) cannot describe complex non- Gaussian diffusion process, many techniques, called as single shell High Angular Resolution Diffusion Imaging (sHARDI) methods, reconstruct the Ensemble Average Propagator (EAP) or its feature Orientation Distribution Function (ODF) from diffusion weighted signals only in single shell. Q-Ball Imaging (QBI) and Diffusion Orientation Transform (DOT) are two famous sHARDI methods. However, these sHARDI methods have some intrinsic modeling errors or need some unreal assumptions. Moreover they are hard to deal with signals from different q-shells. Most recently several novel multiple shell HARDI (mHARDI) methods, including Diffusion Propagator Imaging (DPI), Spherical Polar Fourier Imaging (SPFI) and Simple Harmonic Oscillator based Reconstruction and Estimation (SHORE), were proposed to analytically estimate EAP or ODF from multiple shell (or arbitrarily sampled) signals. These three methods all represent diffusion signal with some basis functions in spherical coordinate and use plane wave formula to analytically solve the Fourier transform. To our knowledge, there is no theoretical analysis and practical comparison among these sHARDI and mHARDI methods. In this paper, we propose a unified computational framework, named Analytical Fourier Transform in Spherical Coordinate (AFT-SC), to perform such theoretical analysis and practical comparison among all these five state-of-the-art diffusion MRI methods. We compare these five methods in both theoretical and experimental aspects. With respect to the theoretical aspect, some criteria are proposed for evaluation and some differences together with some similarities among the methods are highlighted. Regarding the experimental aspect, all the methods are compared in synthetic, phantom and real data. The shortcomings and advantages of each method are highlighted from which SPFI appears to be among the best because it uses an orthonormal basis that completely separates the spherical and radial information.
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Jian Cheng, Sylvain Merlet, Emmanuel Caruyer, Aurobrata Ghosh, Tianzi Jiang, Rachid Deriche,
"Compressive Sensing Ensemble Average Propagator Estimation via L1 Spherical Polar Fourier Imaging",
MICCAI Workshop on Computational Diffusion MRI (CDMRI'11), pp. 108–118, 2011.
[bibtex]
[abstract]
[project]
[citations: 22]
(Oral presentation)
Bibtex
@inproceedings{cheng_L1SPFI_CDMRI2011, author = {Jian Cheng and Sylvain Merlet and Emmanuel Caruyer and Aurobrata Ghosh and Tianzi Jiang and Rachid Deriche}, booktitle = {MICCAI Workshop on Computational Diffusion MRI (CDMRI'11)}, hal_id = {inria-00615437}, pages = {108-118}, pdf = {https://hal.inria.fr/inria-00615437/document}, title = {Compressive Sensing Ensemble Average Propagator Estimation via L1 Spherical Polar Fourier Imaging}, url = {https://hal.archives-ouvertes.fr/inria-00615437}, year = {2011} }Abstract
Since Diffusion Tensor Imaging (DTI) cannot detect the fiber crossing, many new works beyond DTI has been proposed to explore the q-space. Most works, known as single shell High Angular Resolution Imaging (sHARDI), focus on single shell sampling and reconstruct the Orientation Distribution Function (ODF). The ODF, which has no radial information at all, is just one of features of Ensemble Average Propagator (EAP). Diffusion Spectrum Imaging (DSI) is a standard method to estimate EAP via numerical Fourier Transform (FT), which needs lots of samples and is impractical for clinical study. Spherical Polar Fourier Imaging (SPFI) [1,2] was proposed to represent the signal using SPF basis, then the EAP and the ODF have analytical closed forms. So the estimation of the coefficients under SPF basis is very important. In [1,2], the coefficients are estimated based on a standard Least Square (LS) with L2 norm regularization (L2-L2). In this paper, we propose to estimate the coefficients using LS with L1 norm regularization (L2-L1), also named as Least Absolute Selection and Shrinkage Operator (LASSO). And we prove that the L2-L1 estimation of the coefficients is actually the well known Compressive Sensing (CS) method to estimate EAP, which brings lots of Mathematical tools and possibility to improve the sampling scheme in q-space.
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Jian Cheng, Aurobrata Ghosh, Rachid Deriche, Tianzi Jiang,
"Model-Free, Regularized, Fast, and Robust Analytical Orientation Distribution Function Estimation",
Medical Image Computing and Computer-Assisted Intervention (MICCAI'10), vol. 6361, pp. 648–656, sep, 2010.
[bibtex]
[abstract]
[project]
[poster]
[citations: 47]
Bibtex
@inproceedings{Cheng_ODF_MICCAI2010, author = {Jian Cheng and Aurobrata Ghosh and Rachid Deriche and Tianzi Jiang}, booktitle = {Medical Image Computing and Computer-Assisted Intervention (MICCAI'10)}, doi = {10.1007/978-3-642-15705-9_79}, hal_id = {inria-00496929}, month = {sep}, pages = {648-656}, pdf = {https://hal.inria.fr/inria-00496929/document}, title = {Model-Free, Regularized, Fast, and Robust Analytical Orientation Distribution Function Estimation}, url = {https://dx.doi.org/10.1007/978-3-642-15705-9_79}, volume = {6361}, year = {2010} }Abstract
High Angular Resolution Imaging (HARDI) can better explore the complex micro-structure of white matter compared to Diffusion Tensor Imaging (DTI). Orientation Distribution Function (ODF) in HARDI is used to describe the probability of the fiber direction. There are two type definitions of the ODF, which were respectively proposed in Q-Ball Imaging (QBI) and Diffusion Spectrum Imaging (DSI). Some analytical reconstructions methods have been proposed to estimate these two type of ODFs from single shell HARDI data. However they all have some assumptions and intrinsic modeling errors. In this article, we propose, almost without any assumption, a uniform analytical method to estimate these two ODFs from DWI signals in q space, which is based on Spherical Polar Fourier Expression (SPFE) of signals. The solution is analytical and is a linear transformation from the q-space signal to the ODF represented by Spherical Harmonics (SH). It can naturally combines the DWI signals in different Q-shells. Moreover It can avoid the intrinsic Funk- Radon Transform (FRT) blurring error in QBI and it does not need any assumption of the signals, such as the multiple tensor model and mono/multi-exponential decay. We validate our method using synthetic data, phantom data and real data. Our method works well in all experiments, especially for the data with low SNR, low anisotropy and non-exponential decay.
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Jian Cheng, Aurobrata Ghosh, Tianzi Jiang, Rachid Deriche,
"Model-free and Analytical EAP Reconstruction via Spherical Polar Fourier Diffusion MRI",
Medical Image Computing and Computer-Assisted Intervention (MICCAI'10), vol. 6361, pp. 590–597, sep, 2010.
[bibtex]
[abstract]
[project]
[poster]
[citations: 89]
Bibtex
@inproceedings{Cheng_PDF_MICCAI2010, author = {Jian Cheng and Aurobrata Ghosh and Tianzi Jiang and Rachid Deriche}, booktitle = {Medical Image Computing and Computer-Assisted Intervention (MICCAI'10)}, doi = {10.1007/978-3-642-15705-9_72}, hal_id = {inria-00496932}, month = {sep}, pages = {590-597}, pdf = {https://hal.inria.fr/inria-00496932/document}, title = {Model-free and Analytical EAP Reconstruction via Spherical Polar Fourier Diffusion MRI}, url = {https://dx.doi.org/10.1007/978-3-642-15705-9_72}, volume = {6361}, year = {2010} }Abstract
How to estimate the diffusion Ensemble Average Propagator (EAP) from the DWI signals in q-space is an open problem in diffusion MRI field. Many methods were proposed to estimate the Orientation Distribution Function (ODF) that is used to describe the fiber direction. However, ODF is just one of the features of the EAP. Compared with ODF, EAP has the full information about the diffusion process which reflects the complex tissue micro-structure. Diffusion Orientation Transform (DOT) and Diffusion Spectrum Imaging (DSI) are two important methods to estimate the EAP from the signal. However, DOT is based on mono-exponential assumption and DSI needs a lot of samplings and very large b values. In this paper, we propose Spherical Polar Fourier Imaging (SPFI), a novel model-free fast robust analytical EAP reconstruction method, which almost does not need any assumption of data and does not need too many samplings. SPFI naturally combines the DWI signals with different b-values. It is an analytical linear transformation from the q-space signal to the EAP profile represented by Spherical Harmonics (SH). We validated the proposed methods in synthetic data, phantom data and real data. It works well in all experiments, especially for the data with low SNR, low anisotropy, and non-exponential decay.
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Jian Cheng, Aurobrata Ghosh, Tianzi Jiang, Rachid Deriche,
"A Riemannian Framework for Orientation Distribution Function Computing",
Medical Image Computing and Computer-Assisted Intervention (MICCAI'09), vol. 5761, pp. 911–918, 2009.
[bibtex]
[abstract]
[citations: 52]
Bibtex
@inproceedings{JianChengMICCAI2009, author = {Jian Cheng and Aurobrata Ghosh and Tianzi Jiang and Rachid Deriche}, booktitle = {Medical Image Computing and Computer-Assisted Intervention (MICCAI'09)}, doi = {10.1007/978-3-642-04268-3_112}, hal_id = {inria-00424764}, pages = {911-918}, pdf = {https://hal.inria.fr/inria-00424764/document}, title = {A Riemannian Framework for Orientation Distribution Function Computing}, url = {https://dx.doi.org/10.1007/978-3-642-04268-3_112}, volume = {5761}, year = {2009} }Abstract
Compared with Diffusion Tensor Imaging (DTI), High Angular Resolution Imaging (HARDI) can better explore the complex microstructure of white matter. Orientation Distribution Function (ODF) is used to describe the probability of the fiber direction. Fisher information metric has been constructed for probability density family in Information Geometry theory and it has been successfully applied for tensor computing in DTI. In this paper, we present a state of the art Riemannian framework for ODF computing based on Information Geometry and sparse representation of orthonormal bases. In this Riemannian framework, the exponential map, logarithmic map and geodesic have closed forms. And the weighted Frechet mean exists uniquely on this manifold. We also propose a novel scalar measurement, named Geometric Anisotropy (GA), which is the Riemannian geodesic distance between the ODF and the isotropic ODF. The Renyi entropy $H_{1/2}$ of the ODF can be computed from the GA. Moreover, we present an Affine-Euclidean framework and a Log-Euclidean framework so that we can work in an Euclidean space. As an application, Lagrange interpolation on ODF field is proposed based on weighted Frechet mean. We validate our methods on synthetic and real data experiments. Compared with existing Riemannian frameworks on ODF, our framework is model-free. The estimation of the parameters, i.e. Riemannian coordinates, is robust and linear. Moreover it should be noted that our theoretical results can be used for any probability density function (PDF) under an orthonormal basis representation. -
Jian Cheng, Feng Shi, Kun Wang, Ming Song, Jiefeng Jiang, Lijuan Xu, Tianzi Jiang,
"Nonparametric Mean Shift Functional Detection in the Functional Space for Task and Resting-state fMRI",
Workshop on fMRI data analysis: statistical modeling and detection issues in intra- and inter-subject functional MRI data analysis in conjunction with the MICCAI, 2009.
[bibtex]
[abstract]
[citations: 3]
(Oral presentation)
Bibtex
@inproceedings{Cheng_workshopMICCAI2009, author = {Jian Cheng and Feng Shi and Kun Wang and Ming Song and Jiefeng Jiang and Lijuan Xu and Tianzi Jiang}, booktitle = {Workshop on fMRI data analysis: statistical modeling and detection issues in intra- and inter-subject functional MRI data analysis in conjunction with the MICCAI}, hal_id = {inria-00424765}, pdf = {https://hal.inria.fr/inria-00424765/document}, title = {Nonparametric Mean Shift Functional Detection in the Functional Space for Task and Resting-state fMRI}, url = {https://hal.archives-ouvertes.fr/inria-00424765}, year = {2009} }Abstract
In functional Magnetic Resonance Imaging (fMRI) data analysis, normalization of time series is an important and sometimes necessary preprocessing step in many widely used methods. The space of normalized time series with n time points is the unit sphere $S^{n-2}$, named the functional space. Riemannian framework on the sphere, including the geodesic, the exponential map, and the logarithmic map, has been well studied in Riemannian geometry. In this paper, by introducing the Riemannian framework in the functional space, we propose a novel nonparametric robust method, namely Mean Shift Functional Detection (MSFD), to explore the functional space. The first merit of the MSFD is that it does not need many assumptions on data which are assumed in many existing method, e.g. linear addition (GLM, PCA, ICA), uncorrelation (PCA), independence (ICA), the number and the shape of clusters (FCM). Second, MSFD takes into account the spatial information and can be seen as a multivariate extension of the functional connectivity analysis method. It is robust and works well for activation detection in task study even with a biased activation reference. It is also able to find the functional networks in resting-state study without a user-selected "seed" region. Third, it can enhance the boundary between different functional networks. Experiments were conducted on synthetic and real data to compare the performance of the proposed method with GLM and ICA. The experimental results validated the accuracy and robustness of MSFD, not only for activation detection in task study but also for functional network exploration in resting-state study.
Conference Abstracts¶
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Jian Cheng, Peter J. Basser,
"Exploring Local White Matter Geometric Structure in diffusion MRI Using Director Field Analysis",
Scientific Meeting and Exhibition of the ISMRM (ISMRM'17), 2017.
[bibtex]
Bibtex
@conference{cheng:ISMRM2017, author = {Jian Cheng and Peter J. Basser}, booktitle = {Scientific Meeting and Exhibition of the ISMRM (ISMRM'17)}, hal_id = {hal-01511564}, pdf = {https://hal.archives-ouvertes.fr/hal-01511564/document}, title = {Exploring Local White Matter Geometric Structure in diffusion MRI Using Director Field Analysis}, url = {http://submissions.mirasmart.com/ISMRM2017/ViewSubmissionPublic.aspx?sei=YLBxyBRee}, year = {2017} } -
Jian Cheng, Dinggang Shen, Pew-Thian Yap, Peter J. Basser,
"Novel Single and Multiple Shell Gradient Sampling Schemes for Diffusion MRI Using Spherical Codes",
23rd Scientific Meeting and Exhibition of the ISMRM (ISMRM'15), 2015.
[bibtex]
Bibtex
@conference{cheng:ISMRM2015, author = {Jian Cheng and Dinggang Shen and Pew-Thian Yap and Peter J. Basser}, booktitle = {23rd Scientific Meeting and Exhibition of the ISMRM (ISMRM'15)}, hal_id = {hal-01154773}, pdf = {https://hal.archives-ouvertes.fr/hal-01154773/document}, title = {Novel Single and Multiple Shell Gradient Sampling Schemes for Diffusion MRI Using Spherical Codes}, url = {https://hal.archives-ouvertes.fr/hal-01154773}, year = {2015} } -
Jian Cheng, Dinggang Shen, Pew-Thian Yap,
"Joint k-q Space Compressed Sensing for Accelerated Multi-Shell Acquisition and Reconstruction of the diffusion signal and Ensemble Average Propagator",
ISMRM'14, 2014.
[bibtex]
(Oral presentation)
Bibtex
@conference{cheng_ISMRM2014, author = {Jian Cheng and Dinggang Shen and Pew-Thian Yap}, booktitle = {ISMRM'14}, hal_id = {hal-01011893}, pdf = {https://hal.archives-ouvertes.fr/hal-01011893/document}, title = {Joint k-q Space Compressed Sensing for Accelerated Multi-Shell Acquisition and Reconstruction of the diffusion signal and Ensemble Average Propagator}, url = {https://hal.archives-ouvertes.fr/hal-01011893}, year = {2014} } -
Jian Cheng, Pew-Thian Yap, Dinggang Shen,
"Single and Multiple Shell Sampling Design in dMRI Using Spherical code and Mixed Integer Linear Programming",
ISMRM'14, pp. 2558, May, 2014.
[bibtex]
Bibtex
@conference{cheng:ISMRM2014:sampling, address = {Italy}, author = {Jian Cheng and Pew-Thian Yap and Dinggang Shen}, booktitle = {ISMRM'14}, hal_id = {hal-01011892}, month = {May}, pages = {2558}, pdf = {https://hal.archives-ouvertes.fr/hal-01011892/document}, title = {Single and Multiple Shell Sampling Design in dMRI Using Spherical code and Mixed Integer Linear Programming}, url = {https://hal.archives-ouvertes.fr/hal-01011892}, year = {2014} } -
Jian Cheng, Rachid Deriche, Tianzi Jiang, Dinggang Shen, Pew-Thian Yap,
"Non-Local Non-Negative Spherical Deconvolution for Single and Multiple Shell Diffusion MRI",
HARDI Reconstruction Challenge, International Symposium on Biomedical Imaging (ISBI'13), 2013.
[bibtex]
(Honorable Mention; the best technique in terms of local comparison.)
Bibtex
@conference{JianCheng_NNSD_ISBI13, author = {Jian Cheng and Rachid Deriche and Tianzi Jiang and Dinggang Shen and Pew-Thian Yap}, booktitle = {HARDI Reconstruction Challenge, International Symposium on Biomedical Imaging (ISBI'13)}, hal_id = {hal-00967830}, pdf = {https://hal.archives-ouvertes.fr/hal-00967830/document}, title = {Non-Local Non-Negative Spherical Deconvolution for Single and Multiple Shell Diffusion MRI}, url = {https://hal.archives-ouvertes.fr/hal-00967830}, year = {2013} } -
Jian Cheng, Dinggang Shen, Pew-Thian Yap,
"Non-Negative Spherical Deconvolution for Fiber Orientation Distribution Estimation",
ISMRM'13, Apr, 2013.
[bibtex]
Bibtex
@conference{cheng:ISMRM2013, address = {United States}, author = {Jian Cheng and Dinggang Shen and Pew-Thian Yap}, booktitle = {ISMRM'13}, hal_id = {hal-00967831}, month = {Apr}, pdf = {https://hal.archives-ouvertes.fr/hal-00967831/document}, title = {Non-Negative Spherical Deconvolution for Fiber Orientation Distribution Estimation}, url = {https://hal.archives-ouvertes.fr/hal-00967831}, year = {2013} } -
Jian Cheng, Sylvain Merlet, Emmanuel Caruyer, Aurobrata Ghosh, Tianzi Jiang, Rachid Deriche,
"Compressive Sensing Ensemble Average Propagator Estimation via L1 Spherical Polar Fourier Imaging",
ISMRM'11, May, 2011.
[bibtex]
Bibtex
@conference{cheng:ISMRM2011, address = {Montréal, Canada}, author = {Jian Cheng and Sylvain Merlet and Emmanuel Caruyer and Aurobrata Ghosh and Tianzi Jiang and Rachid Deriche}, booktitle = {ISMRM'11}, hal_id = {inria-00615434}, month = {May}, pdf = {https://hal.inria.fr/inria-00615434/document}, title = {Compressive Sensing Ensemble Average Propagator Estimation via L1 Spherical Polar Fourier Imaging}, url = {https://hal.archives-ouvertes.fr/inria-00615434}, year = {2011} } -
Jian Cheng, Aurobrata Ghosh, Tianzi Jiang, Rachid Deriche,
"A Riemannian Framework for Ensemble Average Propagator Computing",
ISMRM'11, 2011.
[bibtex]
Bibtex
@conference{cheng:ISMRM2011:EAP, author = {Jian Cheng and Aurobrata Ghosh and Tianzi Jiang and Rachid Deriche}, booktitle = {ISMRM'11}, hal_id = {inria-00615436}, pdf = {https://hal.inria.fr/inria-00615436/document}, title = {A Riemannian Framework for Ensemble Average Propagator Computing}, url = {https://hal.archives-ouvertes.fr/inria-00615436}, year = {2011} } -
Jian Cheng, Aurobrata Ghosh, Tianzi Jiang, Rachid Deriche,
"Fast, Model-Free, Analytical ODF Reconstruction from the Q-Space Signal",
Proceedings of the Sixteenth Annual Meeting of the Organization for Human Brain Mapping (OHBM'10), 2010.
[bibtex]
Bibtex
@conference{Cheng_ODF_OHBM2010, author = {Jian Cheng and Aurobrata Ghosh and Tianzi Jiang and Rachid Deriche}, booktitle = {Proceedings of the Sixteenth Annual Meeting of the Organization for Human Brain Mapping (OHBM'10)}, hal_id = {inria-00497243}, pdf = {https://hal.inria.fr/inria-00497243/document}, title = {Fast, Model-Free, Analytical ODF Reconstruction from the Q-Space Signal}, url = {https://hal.archives-ouvertes.fr/inria-00497243}, year = {2010} } -
Jian Cheng, Aurobrata Ghosh, Tianzi Jiang, Rachid Deriche,
"Fast, model-free, analytical diffusion PDF profile estimation from the DWI signals",
Proceedings of the Sixteenth Annual Meeting of the Organization for Human Brain Mapping (OHBM'10), 2010.
[bibtex]
Bibtex
@conference{Cheng_PDF_OHBM2010, author = {Jian Cheng and Aurobrata Ghosh and Tianzi Jiang and Rachid Deriche}, booktitle = {Proceedings of the Sixteenth Annual Meeting of the Organization for Human Brain Mapping (OHBM'10)}, hal_id = {inria-00497244}, pdf = {https://hal.inria.fr/inria-00497244/document}, title = {Fast, model-free, analytical diffusion PDF profile estimation from the DWI signals}, url = {https://hal.archives-ouvertes.fr/inria-00497244}, year = {2010} } -
Jian Cheng, Aurobrata Ghosh, Tianzi Jiang, Rachid Deriche,
"Riemannian Median and Its Applications for Orientation Distribution Function Computing",
ISMRM'10, 2010.
[bibtex]
Bibtex
@conference{JianChengISMRM2010, author = {Jian Cheng and Aurobrata Ghosh and Tianzi Jiang and Rachid Deriche}, booktitle = {ISMRM'10}, hal_id = {inria-00497246}, pdf = {https://hal.inria.fr/inria-00497246/document}, title = {Riemannian Median and Its Applications for Orientation Distribution Function Computing}, url = {https://hal.archives-ouvertes.fr/inria-00497246}, year = {2010} }
Theses¶
-
Jian Cheng,
"Estimation and Processing of Ensemble Average Propagator and Its Features in Diffusion MRI",
PhD thesis, Université Nice Sophia Antipolis, and Chinese Academy of Sciences, May, 2012.
[bibtex]
[abstract]
[slides]
[citations: 10]
Bibtex
@phdthesis{thesis_jiancheng2012, author = {Jian Cheng}, hal_id = {tel-00759048}, month = {May}, pdf = {https://tel.archives-ouvertes.fr/tel-00759048/document}, school = {Université Nice Sophia Antipolis, and Chinese Academy of Sciences}, title = {Estimation and Processing of Ensemble Average Propagator and Its Features in Diffusion MRI}, url = {https://hal.archives-ouvertes.fr/tel-00759048}, year = {2012} }Abstract
Diffusion MRI (dMRI) is the unique technique to infer the microstructure of the white matter in vivo and noninvasively, by modeling the diffusion of water molecules. Ensemble Average Propagator (EAP) and Orientation Distribution Function (ODF) are two important Probability Density Functions (PDFs) which reflect the water diffusion. Estimation and processing of EAP and ODF is the central problem in dMRI, and is also the first step for tractography. Diffusion Tensor Imaging (DTI) is the most widely used estimation method which assumes EAP as a Gaussian distribution parameterized by a tensor. Riemannian framework for tensors has been proposed successfully in tensor estimation and processing. However, since the Gaussian EAP assumption is oversimplified, DTI can not reflect complex microstructure like fiber crossing. High Angular Resolution Diffusion Imaging (HARDI) is a category of methods proposed to avoid the limitations of DTI. Most HARDI methods like Q-Ball Imaging (QBI) need some assumptions and only can handle the data from single shell (single $b$ value), which are called as single shell HARDI (sHARDI) methods. However, with the development of scanners and acquisition methods, multiple shell data becomes more and more practical and popular. This thesis focuses on the estimation and processing methods in multiple shell HARDI (mHARDI) which can handle the diffusion data from arbitrary sampling scheme. There are many original contributions in this thesis. -First, we develop the analytical Spherical Polar Fourier Imaging (SPFI), which represents the signal using SPF basis and obtains EAP and its various features including ODFs and some scalar indices like Generalized Fractional Anisotropy (GFA) from analytical linear transforms. In the implementation of SPFI, we present two ways for scale estimation and propose to consider the prior $E(0)=1$ in estimation process. -Second, a novel Analytical Fourier Transform in Spherical Coordinate (AFT-SC) framework is proposed to incorporate many sHARDI and mHARDI methods, explore their relation and devise new analytical EAP/ODF estimation methods. -Third, we present some important criteria to compare different HARDI methods and illustrate their advantages and limitations. -Fourth, we propose a novel diffeomorphism invariant Riemannian framework for ODF and EAP processing, which is a natural generalization of previous Riemannian framework for tensors, and can be used for general PDF computing by representing the square root of the PDF called wavefunction with orthonormal basis. In this Riemannian framework, the exponential map, logarithmic map and geodesic have closed forms, the weighted Riemannian mean and median uniquely exist and can be estimated from an efficient gradient descent. Log-Euclidean framework and Affine- Euclidean framework are developed for fast data processing. -Fifth, we theoretically and experimentally compare the Euclidean metric and Riemannian metric for tensors, ODFs and EAPs. -Finally, we propose the Geodesic Anisotropy (GA) to measure the anisotropy of EAPs, Square Root Parameterized Estimation (SRPE) for nonnegative definite ODF/EAP estimation, weighted Riemannian mean/median for ODF/EAP interpolation, smoothing, atlas estimation. The concept of \emph{reasonable mean value interpolation} is presented for interpolation of general PDF data.