Tuning-free joint sparse recovery via optimization transfer

Multiple measurement vector (MMV) problem addresses the recovery of a set of sparse vectors that have common sparsity pattern. In this paper, we consider a variant of the MMV problem where the common sparsity pattern is obfuscated by an additive noise. Specifically, we study the conditions for perfect reconstruction of the original sparsity pattern. Based on these, we develop a tuning-free algorithm for recovering jointly sparse solutions via the transfer optimization approach. We provide a preliminary numerical evaluation to illustrate our approach.