Recovery Guarantees for Rank Aware Pursuits

Abstract

This letter considers sufficient conditions for sparse recovery in the sparse multiple measurement vector (MMV) problem for some recently proposed rank aware greedy algorithms. Specifically we consider the compressed sensing framework with Gaussian random measurement matrices and show that the rank of the measurement matrix in the noiseless sparse MMV problem allows such algorithms to reduce the effect of the log <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> term that is present in traditional OMP recovery.