Block sparse signal recovery via minimizing the block $q$-ratio sparsity

Zhiyong Zhou

Block sparse signal recovery via minimizing the block $q$-ratio sparsity

Information Theory 2021-03-15 v1 math.IT Optimization and Control

Authors: Zhiyong Zhou

Abstract

In this paper, we propose a method for block sparse signal recovery that minimizes the block $q$ -ratio sparsity $\left(\lVert z\rVert_{2,1}/\lVert z\rVert_{2,q}\right)^{\frac{q}{q-1}}$ with $q\in[0,\infty]$ . For the case of $1<q\leq\infty$ , we present the theoretical analyses and the computing algorithms for both cases of the $\ell_2$ -bounded and $\ell_{2,\infty}$ -bounded noises. The corresponding unconstrained model is also investigated. Its superior performance in block sparse signal reconstruction is demonstrated by numerical experiments.

Keywords

block sparse signal recovery q-ratio sparsity bounded noise unconstrained model numerical experiments

Cite

@article{arxiv.2103.07145,
  title  = {Block sparse signal recovery via minimizing the block $q$-ratio sparsity},
  author = {Zhiyong Zhou},
  journal= {arXiv preprint arXiv:2103.07145},
  year   = {2021}
}

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