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This paper addresses the problems of sparse signal and image recovery using compressive sensing (CS), especially in the case of Gaussian noise. The main contribution of this paper is the proposal of the regularization re-weighted Composite Sine function smoothed  L 0 -norm minimization (RRCSFSL0) algorithm where the Composite Sine function (CSF), the iteratively re-weighted scheme and the regularization mechanism represent the core of an approach to the solution of the problem. Compared with other state-of-the-art functions, the CSF we proposed can better approximate the  L 0 -norm and improve the reconstruction accuracy, the new re-weighted scheme we adopted can promote sparsity and speed up convergence. Moreover, the use of the regularization mechanism makes the RRCSFSL0 algorithm more robust against noise. The performance of the proposed algorithm is verified via numerical experiments in the noise environment. Furthermore, experiments and comparisons demonstrate the superiority of the RRCSFSL0 algorithm in image restoration.

A re-weighted smoothed L0 -norm regularized sparse reconstructed algorithm for linear inverse problems