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Fiber Orientation Distribution Estimation Using a Peaceman-Rachford Splitting Method
Chen, Yannan1; Dai, Yu-Hong2; Han, Deren3
2016
Source PublicationSIAM JOURNAL ON IMAGING SCIENCES
ISSN1936-4954
Volume9Issue:2Pages:573-604
AbstractIn diffusion-weighted magnetic resonance imaging, the estimation of the orientations of multiple nerve fibers in each voxel (the fiber orientation distribution (FOD)) is a critical issue for exploring the connection of cerebral tissue. In this paper, we establish a convex semidefinite programming (CSDP) model for the FOD estimation. One feature of the new model is that it can ensure the statistical meaning of FOD since as a probability density function, FOD must be nonnegative and have a unit mass. To construct such a statistically meaningful FOD, we consider its approximation by a sum of squares (SOS) polynomial and impose the unit-mass by a linear constraint. Another feature of the new model is that it introduces a new regularization based on the sparsity of nerve fibers. Due to the sparsity of the orientations of nerve fibers in cerebral white matter, a heuristic regularization is raised, which is inspired by the Z-eigenvalue of a symmetric tensor that closely relates to the SOS polynomial. To solve the CSDP efficiently, we propose a new Peaceman-Rachford splitting method and prove its global convergence. Numerical experiments on synthetic and real-world human brain data show that, when compared with some existing approaches for fiber estimations, the new method gives a sharp and smooth FOD. Further, the proposed Peaceman-Rachford splitting method is shown to have good numerical performances comparing several existing methods.
Keywordfiber orientation distribution magnetic resonance imaging Peaceman-Rachford splitting method positive semidefinite tensor semidefinite programming sum of squares polynomial
DOI10.1137/15M1026626
Language英语
Funding ProjectNational Natural Science Foundation of China[11401539] ; Development Foundation for Excellent Youth Scholars of Zhengzhou University[1421315070] ; Hong Kong Polytechnic University Postdoctoral Fellowship ; National Key Basic Research Program of China[2015CB856000] ; China National Funds for Distinguished Young Scientists[11125107] ; Chinese NSF[11331012] ; Chinese NSF[81173663] ; PAPD of Jiangsu Higher Education Institutions ; Natural Science Foundation of China[11371197] ; Natural Science Foundation of China[11431002]
WOS Research AreaComputer Science ; Mathematics ; Imaging Science & Photographic Technology
WOS SubjectComputer Science, Artificial Intelligence ; Computer Science, Software Engineering ; Mathematics, Applied ; Imaging Science & Photographic Technology
WOS IDWOS:000385275400004
PublisherSIAM PUBLICATIONS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/23777
Collection计算数学与科学工程计算研究所
Corresponding AuthorChen, Yannan
Affiliation1.Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Peoples R China
2.Chinese Acad Sci, Inst Computat Math, Beijing 100190, Peoples R China
3.Nanjing Normal Univ, Sch Math Sci, Key Lab NSLSCS Jiangsu Prov, Nanjing 210023, Jiangsu, Peoples R China
Recommended Citation
GB/T 7714
Chen, Yannan,Dai, Yu-Hong,Han, Deren. Fiber Orientation Distribution Estimation Using a Peaceman-Rachford Splitting Method[J]. SIAM JOURNAL ON IMAGING SCIENCES,2016,9(2):573-604.
APA Chen, Yannan,Dai, Yu-Hong,&Han, Deren.(2016).Fiber Orientation Distribution Estimation Using a Peaceman-Rachford Splitting Method.SIAM JOURNAL ON IMAGING SCIENCES,9(2),573-604.
MLA Chen, Yannan,et al."Fiber Orientation Distribution Estimation Using a Peaceman-Rachford Splitting Method".SIAM JOURNAL ON IMAGING SCIENCES 9.2(2016):573-604.
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