Detection of time-varying support via rank evolution approach for effective joint sparse recovery

Abstract

Efficient recovery of sparse signals from few linear projections is a primary goal in a number of applications, most notably in a recently-emerged area of compressed sensing. The multiple measurement vector (MMV) joint sparse recovery is an extension of the single vector sparse recovery problem to the case when a set of consequent measurements share the same support. In this contribution we consider a modification of the MMV problem where the signal support can change from one block of data to another and the moment of change is not known in advance. We propose an approach for the support change detection based on the sequential rank estimation of a windowed block of the measurement data. We show that under certain conditions it allows for an unambiguous determination of the moment of change, provided that the consequent data vectors are incoherent to each other.