Fixed-Time Stable Neurodynamic Flow to Sparse Signal Recovery via Nonconvex L1-β2-Norm

You Zhao; Xiaofeng Liao; Xing He

doi:10.1162/neco_a_01508

Fixed-Time Stable Neurodynamic Flow to Sparse Signal Recovery via Nonconvex L1-β2-Norm

Neural Comput. 2022 Jul 14;34(8):1727-1755. doi: 10.1162/neco_a_01508.

Authors

You Zhao¹, Xiaofeng Liao², Xing He³

Affiliations

¹ Key Laboratory of Dependable Services Computing in Cyber Physical Society-Ministry of Education, College of Computer Science, Chongqing University, Chongqing 400044, China Zhaoyou1991sdtz@163.com.
² IEEE Fellow, and Key Laboratory of Dependable Services Computing in Cyber Physical Society-Ministry of Education, College of Computer Science, Chongqing University, Chongqing 400044, China xfliao@cqu.edu.cn.
³ Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronics and Information Engineering, Southwest University, Chongqing 400715, China hexingdoc@swu.edu.cn.

PMID: 35798330
DOI: 10.1162/neco_a_01508

Abstract

This letter develops a novel fixed-time stable neurodynamic flow (FTSNF) implemented in a dynamical system for solving the nonconvex, nonsmooth model L1-β2, β∈[0,1] to recover a sparse signal. FTSNF is composed of many neuron-like elements running in parallel. It is very efficient and has provable fixed-time convergence. First, a closed-form solution of the proximal operator to model L1-β2, β∈[0,1] is presented based on the classic soft thresholding of the L1-norm. Next, the proposed FTSNF is proven to have a fixed-time convergence property without additional assumptions on the convexity and strong monotonicity of the objective functions. In addition, we show that FTSNF can be transformed into other proximal neurodynamic flows that have exponential and finite-time convergence properties. The simulation results of sparse signal recovery verify the effectiveness and superiority of the proposed FTSNF.