Greedy Pursuits Assisted Basis Pursuit for reconstruction of joint-sparse signals

Abstract

Distributed Compressive Sensing (DCS) is an extension of compressive sensing from single measurement vector problem to Multiple Measurement Vectors (MMV) problem. In DCS, several reconstruction algorithms have been proposed to reconstruct the joint-sparse signal ensemble. However, most of them are designed for signal ensemble sharing common support. Since the assumption of common sparsity pattern is very restrictive, we are more interested in signal ensemble containing both common and innovation components. With a goal of proposing an MMV-type algorithm that is robust to outliers (absence of common sparsity pattern), we propose Greedy Pursuits Assisted Basis Pursuit for Multiple Measurement Vectors (GPABP-MMV). It employs modified basis pursuit and MMV versions of multiple greedy pursuits. We also formulate the exact reconstruction conditions and the reconstruction error bound for GPABP-MMV. GPABP-MMV is suitable for a variety of applications including time-sequence reconstruction of video frames, reconstruction of ECG signals, etc.