Recovery of correlated row sparse signals using smoothed L0-norm algorithm

Abstract

Distributed compressed sensing (DCS) is an emerging research field which exploits both intra-signal and inter-signal correlations. This paper focuses on the recovery of the sparse signals which can be modeled as joint sparsity model (JSM) 2 with different nonzero coefficients in the same location set. Smoothed L0 norm algorithm is utilized to convert a non-convex and intractable mixed L2,0 norm optimization problem into a solvable one. Compared with a series of single-measurement-vector problems, the proposed approach can obtain a better reconstruction performance by exploiting the inter-signal correlations. Simulation results show that our algorithm outperforms L1,1 norm optimization for both noiseless and noisy cases and is more robust against thermal noise compared with L1,2 recovery. Besides, with the help of the core concept of modified compressed sensing (CS) that utilizes partial known support as side information, we also extend this algorithm to decode correlated row sparse signals generated following JSM 1.