TY - JOUR
T1 - Vector minimax concave penalty for sparse representation
AU - Wang, Shibin
AU - Chen, Xuefeng
AU - Dai, Weiwei
AU - Selesnick, Ivan W.
AU - Cai, Gaigai
AU - Cowen, Benjamin
N1 - Funding Information:
This work was partly supported by National Natural Science Foundation of China under Grand 51605366 and 51835009 , National Key Basic Research Program of China under Grant 2015CB057400 , China Postdoctoral Science Foundation under Grand 2016M590937 and 2017T100740 , the Fundamental Research Funds for the Central Universities , and the open fund of Zhejiang Provincial Key Laboratory of Laser Processing Robot/Key Laboratory of Laser Precision Processing and Detection .
Publisher Copyright:
© 2018 Elsevier Inc.
PY - 2018/12
Y1 - 2018/12
N2 - This paper proposes vector minimax concave (VMC) penalty for sparse representation using tools of Moreau envelope. The VMC penalty is a weighted MC function; by fine tuning the weight of the VMC penalty with given strategy, the VMC regularized least squares problem shares the same global minimizers with the L0 regularization problem but has fewer local minima. Facilitated by the alternating direction method of multipliers (ADMM), the VMC regularization problem can be tackled as a sequence of convex sub-problems, each of which can be solved fast. Theoretical analysis of ADMM shows that the convergence of solving the VMC regularization problem is guaranteed. We present a series of numerical experiments demonstrating the superior performance of the VMC penalty and the ADMM algorithm in broad applications for sparse representation, including sparse denoising, sparse deconvolution, and missing data estimation.
AB - This paper proposes vector minimax concave (VMC) penalty for sparse representation using tools of Moreau envelope. The VMC penalty is a weighted MC function; by fine tuning the weight of the VMC penalty with given strategy, the VMC regularized least squares problem shares the same global minimizers with the L0 regularization problem but has fewer local minima. Facilitated by the alternating direction method of multipliers (ADMM), the VMC regularization problem can be tackled as a sequence of convex sub-problems, each of which can be solved fast. Theoretical analysis of ADMM shows that the convergence of solving the VMC regularization problem is guaranteed. We present a series of numerical experiments demonstrating the superior performance of the VMC penalty and the ADMM algorithm in broad applications for sparse representation, including sparse denoising, sparse deconvolution, and missing data estimation.
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U2 - 10.1016/j.dsp.2018.08.021
DO - 10.1016/j.dsp.2018.08.021
M3 - Article
AN - SCOPUS:85053290402
SN - 1051-2004
VL - 83
SP - 165
EP - 179
JO - Digital Signal Processing: A Review Journal
JF - Digital Signal Processing: A Review Journal
ER -