  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.
