Splitting Matching Pursuit Method for Reconstructing Sparse Signal in Compressed Sensing

Abstract

In this paper, a novel method named as splitting matching pursuit (SMP) is proposed to reconstruct $K$-sparse signal in compressed sensing. The proposed method selects $Fl$ $(Fl>2K)$ largest components of the correlation vector $c$, which are divided into $F$ split sets with equal length $l$. The searching area is thus expanded to incorporate more candidate components, which increases the probability of finding the true components at one iteration. The proposed method does not require the sparsity level $K$ to be known in prior. The Merging, Estimation and Pruning steps are carried out for each split set independently, which makes it especially suitable for parallel computation. The proposed SMP method is then extended to more practical condition, e.g. the direction of arrival (DOA) estimation problem in phased array radar system using compressed sensing. Numerical simulations show that the proposed method succeeds in identifying multiple targets in a sparse radar scene, outperforming other OMP-type methods. The proposed method also obtains more precise estimation of DOA angle using one snapshot compared with the traditional estimation methods such as Capon, APES (amplitude and phase estimation) and GLRT (generalized likelihood ratio test) based on hundreds of snapshots.