Performance Analysis of Joint-Sparse Recovery from Multiple Measurements and Prior Information via Convex Optimization

TL;DR

This paper analyzes the use of convex optimization for joint-sparse recovery in compressed sensing with multiple measurements and prior information, providing conditions for successful reconstruction and demonstrating improved performance through experiments.

Contribution

It derives necessary and sufficient conditions for signal recovery and establishes measurement bounds, highlighting how prior information enhances compressed sensing.

Findings

Derived exact recovery conditions using conic geometry

Established measurement bounds for successful reconstruction

Validated effectiveness through experimental results

Abstract

We address the problem of compressed sensing with multiple measurement vectors associated with prior information in order to better reconstruct an original sparse matrix signal. $\ell_{2,1}-\ell_{2,1}$ minimization is used to emphasize co-sparsity property and similarity between matrix signal and prior information. We then derive the necessary and sufficient condition of successfully reconstructing the original signal and establish the lower and upper bounds of required measurements such that the condition holds from the perspective of conic geometry. Our bounds further indicates what prior information is helpful to improve the the performance of CS. Experimental results validates the effectiveness of all our findings.