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

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$q\in[0,\infty]$\mathrm{.}Forthecaseof$1<q\leq\infty$, we present the theoretical analyses and the computing algorithms for both cases of the ${\mathrm{\ell }}_2$-bounded and ${\mathrm{\ell }}_{2,\mathrm{\infty }}$-bounded noises. The corresponding unconstrained model is also investigated. Its superior performance in block sparse signal reconstruction is demonstrated by numerical experiments.