Effective zero-norm minimization algorithms for noisy compressed sensing

Abstract This paper proposes two new algorithms, namely (i) SSReL1Min(CVX)-Scalar-Sign function-based Reweighted L 1 − norm Minimization algorithm combined with Disciplined Convex Programming for a high-performance L 0 − norm Minimization algorithm and (ii) SSReL1Min(MBB) - SSReL1Min algorithm combined with modified Barzilai-Borwein algorithm for a computational fast L 0 − norm Minimization algorithm (without significantly sacrificing the performance). Based on the proposed L 0 − norm minimization algorithm, this paper also presents an upgraded compressed sensing to improve its performance on the recovery of noisy signals. The proposed L 0 − norm minimization algorithm includes a new optimal scalar-sign function-based weighting (in the least squares sense), as well as a new and systematic mapping mechanism in pre- and post-processing, for noisy compressed sensing. This improvement is further confirmed by experimental results. Comparisons with different state-of-the-art solvers are also included, to show that the proposed method outperforms existing ones.