A Reweighted Symmetric Smoothed Function Approximating L0-Norm Regularized Sparse Reconstruction Method

Abstract

Sparse-signal recovery in noisy conditions is a problem that can be solved with current compressive-sensing (CS) technology. Although current algorithms based on L 1 regularization can solve this problem, the L 1 regularization mechanism cannot promote signal sparsity under noisy conditions, resulting in low recovery accuracy. Based on this, we propose a regularized reweighted composite trigonometric smoothed L 0 -norm minimization (RRCTSL0) algorithm in this paper. The main contributions of this paper are as follows: (1) a new smoothed symmetric composite trigonometric (CT) function is proposed to fit the L 0 -norm; (2) a new reweighted function is proposed; and (3) a new L 0 regularization objective function framework is constructed based on the idea of T i k h o n o v regularization. In the new objective function framework, Contributions (1) and (2) are combined as sparsity regularization terms, and errors as deviation terms. Furthermore, the conjugate-gradient (CG) method is used to optimize the objective function, so as to achieve accurate recovery of sparse signal and image under noisy conditions. The numerical experiments on both the simulated and real data verify that the proposed algorithm is superior to other state-of-the-art algorithms, and achieves advanced performance under noisy conditions.

Fast, Efficient, and Viable Compressed Sensing, Low-Rank, and Robust Principle Component Analysis Algorithms for Radar Signal Processing

“…Depending on the problem size, greedy algorithms are fast and of low computational complexity. However, they are known to be sensitive to noise [45,46]. Another issue arises in the context of closely spaced radar targets, for which greedy algorithms tend to merge such targets into a single one.…”

“…The 1 -and nuclear norms are the tightest convex approximations of the 0 -norm and rank function, respectively [45,60]. However, it was found that the reconstruction error of solutions derived from convex relaxed approaches can be further reduced by applying smoothed 0 -and smoothed rank approximation frameworks [45,46,[61][62][63][64]. Their purpose is to enforce a stricter sparsity or rank measure compared to the 1 -and nuclear norm.…”

“…The next question of course is how to choose the regularization parameter λ and thus which shrinkage a = µλ should be applied. The usage of a ST operator causes the singular values of the optimal solution L opt generated by the turbo framework (45) to possess an offset of a for every singular value compared with the true solution L. Too much shrinkage results in a large bias, while too little results in a slow convergence rate. As such, an optimal constant λ does not exists, rather λ would need to be adjusted in every iteration.…”

A Novel Image-Restoration Method Based on High-Order Total Variation Regularization Term

“…In the field of electronics and information, signal processing is a hot research topic, and as a special signal, the study of image has attracted the attention of scholars all over the world [1][2][3]. In image processing, image restoration is one of the most important issues and this issue has received extensive attention in the past few decades [4][5][6][7][8][9][10][11]. Image restoration is a technology that uses degraded images and some prior information to restore and reconstruct clear images, to improve image quality.…”