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

Abstract

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.

Sparse Decomposition of Heart Rate Using a Bernoulli-Gaussian Model: Application to Sleep Apnoea Detection

“…Different approaches have been proposed to find an approximate solution of or of the (similar) problem: or, in the noiseless case: which are NP-hard. Among others, one strategy is to approximate the norm by a differentiable version [ 29 , 30 , 31 , 32 ]. Another possibility, widely explored, is to use a greedy strategy in the spirit of matching pursuit [ 33 ], initially proposed in the underdetermined case, (sparse coding), which evolved to orthogonal matching pursuit (OMP) and orthogonal least squares (OLS).…”

Sparsity-promoting algorithms for the discovery of informative Koopman-invariant subspaces

“…Here a w,0 i w i |a i | 0 , |a i | 0 is one if a i / = 0 and zero otherwise. Note that this pseudo-norm can be viewed as a limiting case of a weighted composite sine function smoothed 0 regularization (Wang et al 2019).…”

“…Note that this pseudo-norm can be viewed as a limiting case of a weighted composite sine function smoothed regularization (Wang et al. 2019).…”

LPFS: Learnable Polarizing Feature Selection for Click-Through Rate Prediction

“…Following work [23] studied the convergence properties of the above smoothed-ℓ 0 and find that under some mild constraints, the convergence is guaranteed. Afterwards, various smoothed-ℓ 0 functions had been proposed and studied for compressed sensing, such as 𝑓 𝜖 (𝑥) = sin arctan |𝑥 | 𝜖 [32], 𝑓 𝜖 (𝑥) = tanh 𝑥 2 2𝜖 2 [37] and [34]. All these functions have following important property:…”