A Neurodynamic Algorithm for Sparse Signal Reconstruction with Finite-Time Convergence

In this paper, a neurodynamic algorithm with finite-time convergence to solve L1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L_{\mathrm{{1}}}}$$\end{document}-minimization problem is proposed for sparse signal reconstruction which is based on projection neural network (PNN). Compared with the existing PNN, the proposed algorithm is combined with the sliding mode technique in control theory. Under certain conditions, the stability of the proposed algorithm in the sense of Lyapunov is analyzed and discussed, and then the finite-time convergence of the proposed algorithm is proved and the setting time bound is given. Finally, simulation results on a numerical example and a contrast experiment show the effectiveness and superiority of our proposed neurodynamic algorithm.