Block-Sparse Recovery With Optimal Block Partition

This paper presents a convex recovery method for block-sparse signals whose block partitions are unknown priori. We first introduce nonconvex penalty function, where the partition is adapted signal of interest by minimizing mixed $\ell _{2}/\ell _{1}$ norm over all possible partitions. Then, exploiting variational representation _{2}$ norm, we derive proposed function as suitable relaxation one. For model designed with penalty, develop an iterative algorithm which guaranteed to converge globally optimal solution. Numerical experiments demonstrate effectiveness method.