Minimization of the q-ratio sparsity with 1 < q ≤ ∞ for signal recovery

2020/10/07 by Zhiyong Zhou, Jun Yu, Zhou, Zhiyong +1 · 2 citations
Computer Science · Engineering · Mathematics · #Algorithm #Applied mathematics #Blind Source Separation Techniques #Combinatorics #Compressed sensing #Computer science #Discrete mathematics #Image and Signal Denoising Methods #Invariant (physics) #Mathematical optimization #Mathematical physics #Mathematics #Minification #Nonlinear programming #Nonlinear system #Physics #SIGNAL (programming language) #Scale invariance #Signal recovery #Singular value #Sparse and Compressive Sensing Techniques #Statistics #cs.IT #math.IT #msc:94A12 #msc:94A20

paper · pdf · doi:10.48550/arxiv.2010.03402

published in arXiv (Cornell University) (Cornell University) · 21 pages, 11 figures

arxiv created 2020/10/07 · openalex publication_date 2020/10/07 · arxiv updated 2020/10/08 · openalex created_date 2020/10/15 · openalex updated_date 2026/08/06

Abstract

In this paper, we propose a general scale invariant approach for sparse signal recovery via the minimization of the q-ratio sparsity. When 1 &lt; q ≤ ∞, both the theoretical analysis based on q-ratio constrained minimal singular values (CMSV) and the practical algorithms via nonlinear fractional programming are presented. Numerical experiments are conducted to demonstrate the advantageous performance of the proposed approaches over the state-of-the-art sparse recovery methods.

Citations

• Nearly unbiased variable selection under minimax concave penalty
• Sparse Approximate Solutions to Linear Systems
• Sparse filtering with the generalized lp / lq norm and its applications to the condition monitoring of rotating machinery

Cited by

• Difference-of-Convex Elastic Net for Compressed Sensing
• An Efficient ADMM Method for Ratio-Type Nonconvex and Nonsmooth Minimization in Sparse Recovery

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