Anti-noise-folding regularized subspace pursuit recovery algorithm for noisy sparse signals

Denoising recovery algorithms are very important for the development of compressed sensing (CS) theory and its applications. Considering the noise present in both the original sparse signal x and the compressive measurements y, we propose a novel denoising recovery algorithm, named Regularized Subspace Pursuit (RSP). Firstly, by introducing a data pre-processing operation, the proposed algorithm alleviates the noise-folding effect caused by the noise added to x. Then, the indices of the nonzero elements in x are identified by regularizing the chosen columns of the measurement matrix. Afterwards, the chosen indices are updated by retaining only the largest entries in the Minimum Mean Square Error (MMSE) estimated signal. Simulation results show that, compared with the traditional orthogonal matching pursuit (OMP) algorithm, the proposed RSP algorithm increases the successful recovery rate (and reduces the reconstruction error) by up to 50% and 86% (35% and 65%) in high noise level scenarios and inadequate measurements scenarios, respectively.