2016/05/02 by Zhuo-Xu Cui, Zhuo‐Xu Cui, Cui, Zhuo-Xu +2
Computer Science · Engineering · Mathematics · #Algorithm #Applied mathematics #Artificial intelligence #Blind Source Separation Techniques #Combinatorics #Compressed sensing #Computer science #Eigenvalues and eigenvectors #FOS: Mathematics #Hankel matrix #Low-rank approximation #Mathematical analysis #Mathematical optimization #Mathematics #Matrix (chemical analysis) #Matrix completion #Matrix norm #Minification #Norm (philosophy) #Optimization and Control (math.OC) #Penalty method #Photoacoustic and Ultrasonic Imaging #Physics #Rank (graph theory) #Regularization (linguistics) #Sparse and Compressive Sensing Techniques #Stationary point #Subsequence #math.OC
paper · pdf · doi:10.48550/arxiv.1605.00479
published in arXiv (Cornell University) (Cornell University) · 19 pages,4 figures
arxiv created 2016/05/02 · openalex publication_date 2016/05/02 · arxiv updated 2016/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
In this paper, nonconvex and nonsmooth models for compressed sensing (CS) and low rank matrix completion (MC) is studied. The problem is formulated as a nonconvex regularized leat square optimization problems, in which the l0-norm and the rank function are replaced by l1-norm and nuclear norm, and adding a nonconvex penalty function respectively. An alternating minimization scheme is developed, and the existence of a subsequence, which generate by the alternating algorithm that converges to a critical point, is proved. The NSP, RIP, and RIP condition for stable recovery guarantees also be analysed for the nonconvex regularized CS and MC problems respectively. Finally, the performance of the proposed method is demonstrated through experimental results.