An Efficient Greedy Algorithm for Sparse Recovery in Noisy Environment

Abstract: Greedy algorithm are in widespread use for sparse recovery because of its efficiency. But some evident flaws exists in most popular greedy algorithms, such as CoSaMP, which includes unreasonable demands on prior knowledge of target signal and excessive sensitivity to random noise. A new greedy algorithm called AMOP is proposed in this paper to overcome these obstacles. Unlike CoSaMP, AMOP can extract necessary information of target signal from sample data adaptively and operate normally with little prior knowledge. The recovery error of AMOP is well controlled when random noise is presented and fades away along with increase of SNR. Moreover, AMOP has good robustness on detailed setting of target signal and less dependence on structure of measurement matrix. The validity of AMOP is verified by theoretical derivation. Extensive simulation experiment is performed to illustrate the advantages of AMOP over CoSaMP in many respects. AMOP is a good candidate of practical greedy algorithm in various applications of Compressed Sensing.