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

Zhiyong Zhou

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arXiv · 2103.07145

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

Zhiyong Zhou

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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.

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Zhiyong Zhou. 2021-03-12. Block sparse signal recovery via minimizing the block $q$-ratio sparsity. https://arxiv.org/abs/2103.07145

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