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

Abstract

In this paper, we propose a method for block sparse signal recovery that minimizes the block $q$-ratio sparsity ${\left(\Vert z{\Vert }_{2,1}/\Vert z{\Vert }_{2,q}\right)}^{\frac{q}{q-1}}$ with $q\in [0,\infty ]$. For the case of $1<q\le \infty$, 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.