Nonconvex fraction function recovery sparse signal by convex optimization algorithm

TL;DR

This paper introduces two convex iterative FP thresholding algorithms for sparse signal recovery, with proven convergence and adaptive parameter selection, demonstrating superior performance in numerical simulations.

Contribution

The paper develops two novel convex iterative FP thresholding algorithms with convergence guarantees and adaptive parameter choice for sparse signal recovery.

Findings

Algorithm-Scheme 2 performs well in sparse signal recovery.

Convergence of Scheme 1 is theoretically proven.

Numerical tests confirm the effectiveness of Scheme 2.

Abstract

In this paper, we will generate a convex iterative FP thresholding algorithm to solve the problem $(FP^{\lambda}_{a})$. Two schemes of convex iterative FP thresholding algorithms are generated. One is convex iterative FP thresholding algorithm-Scheme 1 and the other is convex iterative FP thresholding algorithm-Scheme 2. A global convergence theorem is proved for the convex iterative FP thresholding algorithm-Scheme 1. Under an adaptive rule, the convex iterative FP thresholding algorithm-Scheme 2 will be adaptive both for the choice of the regularized parameter $\lambda$ and parameter $a$. These are the advantages for our two schemes of convex iterative FP thresholding algorithm compared with our previous proposed two schemes of iterative FP thresholding algorithm. At last, we provide a series of numerical simulations to test the performance of the convex iterative FP thresholding algorithm-Scheme 2, and the simulation results show that our convex iterative FP thresholding algorithm-Scheme 2 performs very well in recovering a sparse signal.