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

TL;DR

This paper introduces a novel method for block sparse signal recovery that minimizes the block q-ratio sparsity, providing theoretical analysis, algorithms, and demonstrating superior reconstruction performance through numerical experiments.

Contribution

It proposes a new block q-ratio sparsity minimization approach with theoretical analysis and algorithms for noisy environments, enhancing block sparse signal recovery.

Findings

The method effectively recovers block sparse signals in noisy conditions.

Theoretical analysis supports the proposed approach.

Numerical experiments show improved reconstruction performance.

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.