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

You Zhao, Xiaofeng Liao, Xing He

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 finitetime convergence properties. The simulation results of sparse signal recovery verify the effectiveness and superiority of the proposed FTSNF.