Split Bregman algorithms for multiple measurement vector problem

Abstract

The standard sparse representation aims to reconstruct sparse signal from single measurement vector which is known as SMV model. In some applications, the SMV model extend to the multiple measurement vector (MMV) model, in which the signal consists of a set of jointly sparse vectors. In this paper, efficient algorithms based on split Bregman iteration are proposed to solve the MMV problems with both constrained form and unconstrained form. The convergence of the proposed algorithms is also discussed. Moreover, the proposed algorithms are used in magnetic resonance imaging reconstruction. Numerical results show the effectiveness of the proposed algorithms.