An Improved RIP-Based Performance Guarantee for Sparse Signal Reconstruction via Subspace Pursuit

Abstract

Subspace pursuit (SP) is a well-known greedy algorithm capable of reconstructing a sparse signal vector from a set of incomplete measurements. In this paper, by exploiting an approximate orthogonality condition characterized in terms of the achievable angles between two compressed orthogonal sparse vectors, we show that perfect signal recovery in the noiseless case, as well as stable signal recovery in the noisy case, is guaranteed if the sensing matrix satisfies RIP of order 3K with RIC delta(3K) <= 0.2412. Our work improves the best-known existing results, namely, delta(3K) < 0.165 for the noiseless case [3] and delta(3K) < 0.139 when noise is present [4]. In addition, for the noisy case we derive a reconstruction error upper bound, which is shown to be smaller as compared to the bound reported in [4].