Vector minimax concave penalty for sparse representation

Shibin Wang, Xuefeng Chen, Weiwei Dai, Ivan W. Selesnick, Gaigai Cai, Benjamin Cowen

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)165-179
Number of pages15
JournalDigital Signal Processing: A Review Journal
StatePublished - Dec 2018

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Signal Processing
  • Applied Mathematics
  • Electrical and Electronic Engineering
  • Computer Vision and Pattern Recognition
  • Statistics, Probability and Uncertainty
  • Computational Theory and Mathematics


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