Nonconvex Splitting for Regularized Low-Rank plus Sparse Decomposition

被引:148
作者
Chartrand, Rick [1 ]
机构
[1] Los Alamos Natl Lab, Div Theoret, Los Alamos, NM 87545 USA
关键词
Algorithms; compressed sensing; optimization; principal component analysis; video signal processing; RECONSTRUCTION; ALGORITHM;
D O I
10.1109/TSP.2012.2208955
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
We develop new nonconvex approaches for matrix optimization problems involving sparsity. The heart of the methods is a new, nonconvex penalty function that is designed for efficient minimization by means of a generalized shrinkage operation. We apply this approach to the decomposition of video into low rank and sparse components, which is able to separate moving objects from the stationary background better than in the convex case. In the case of noisy data, we add a nonconvex regularization, and apply a splitting approach to decompose the optimization problem into simple, parallelizable components. The nonconvex regularization ameliorates contrast loss, thereby allowing stronger denoising without losing more signal to the residual.
引用
收藏
页码:5810 / 5819
页数:10
相关论文
共 21 条
[1]  
[Anonymous], 1998, Variational Analysis
[2]  
[Anonymous], UILUENG092214
[3]   A SINGULAR VALUE THRESHOLDING ALGORITHM FOR MATRIX COMPLETION [J].
Cai, Jian-Feng ;
Candes, Emmanuel J. ;
Shen, Zuowei .
SIAM JOURNAL ON OPTIMIZATION, 2010, 20 (04) :1956-1982
[4]   Robust uncertainty principles:: Exact signal reconstruction from highly incomplete frequency information [J].
Candès, EJ ;
Romberg, J ;
Tao, T .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2006, 52 (02) :489-509
[5]   Robust Principal Component Analysis? [J].
Candes, Emmanuel J. ;
Li, Xiaodong ;
Ma, Yi ;
Wright, John .
JOURNAL OF THE ACM, 2011, 58 (03)
[6]   Exact Matrix Completion via Convex Optimization [J].
Candes, Emmanuel J. ;
Recht, Benjamin .
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2009, 9 (06) :717-772
[7]  
Chartrand R, 2007, IEEE IMAGE PROC, P293
[8]   Iteratively reweighted algorithms for compressive sensing [J].
Chartrand, Rick ;
Yin, Wotao .
2008 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING, VOLS 1-12, 2008, :3869-+
[9]   Exact reconstruction of sparse signals via nonconvex minimization [J].
Chartrand, Rick .
IEEE SIGNAL PROCESSING LETTERS, 2007, 14 (10) :707-710
[10]   Restricted isometry properties and nonconvex compressive sensing [J].
Chartrand, Rick ;
Staneva, Valentina .
INVERSE PROBLEMS, 2008, 24 (03)