Fiber Orientation Distribution Estimation Using a Peaceman-Rachford Splitting Method

doi:10.1137/15M1026626

	Fiber Orientation Distribution Estimation Using a Peaceman-Rachford Splitting Method
	Chen, Yannan 1; Dai, Yu-Hong2 ; Han, Deren 3
	2016
发表期刊	SIAM JOURNAL ON IMAGING SCIENCES
ISSN	1936-4954
卷号	9 期号:2 页码:573-604
摘要	In 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.
关键词	fiber orientation distribution magnetic resonance imaging Peaceman-Rachford splitting method positive semidefinite tensor semidefinite programming sum of squares polynomial
DOI	10.1137/15M1026626
语种	英语
资助项目	National 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研究方向	Computer Science ; Mathematics ; Imaging Science & Photographic Technology
WOS类目	Computer Science, Artificial Intelligence ; Computer Science, Software Engineering ; Mathematics, Applied ; Imaging Science & Photographic Technology
WOS记录号	WOS:000385275400004
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/23777
专题	计算数学与科学工程计算研究所
通讯作者	Chen, Yannan
作者单位	1.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
推荐引用方式 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.