A Nonconvex Nonsmooth Regularization Method for Compressed Sensing and Low-Rank Matrix Completion

2016/05/02 by Zhuo‐Xu Cui, Cui, Zhuo-Xu, Qibin Fan +1
Computer Science · Engineering · #Blind Source Separation Techniques #FOS: Mathematics #Optimization and Control (math.OC) #Photoacoustic and Ultrasonic Imaging #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1605.00479

openalex publication_date 2016/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• New bounds on the restricted isometry constant δ2k
• Nearly unbiased variable selection under minimax concave penalty
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• A Statistical View of Some Chemometrics Regression Tools
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• Stable signal recovery from incomplete and inaccurate measurements

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