Exact recoverability analysis for joint sparse optimization with missing measurements

Abstract

Motivated by many applications which involve the sparse signals recovery, the joint sparse optimization problem or MMV (multiple measurement vectors) problem has been drawn more and more attentions in recently studies. A special and hot issue in MMV problem is how to find the sparse solutions when not all the entries of the measurements is fully observed, but some of them are missing. Although several works have already focused on this problem and some algorithms have also been proposed to solve the corresponding models, the analysis of recovery ability to the basic model has still not been provided. Thus, this paper presents theoretical analysis of recovery guarantees for joint sparse optimization problem with missing measurements. Simulation results are presented to verify the validity of our theories and also to illustrate the potential applications of our framework.