Inverse-free distributed neurodynamic optimization algorithms for sparse reconstruction

Abstract

This article proposes three novel inverse-free distributed neurodynamic optimization algorithms to reconstruct sparse signal and image by addressing the L1-minimization problems. Based on multi-agent consensus theory, we successfully transform the original L1-minimization problem into a distributed optimization model. To tackle such model, a three-layer inverse-free distributed algorithm is proposed by using projection operator and derivative feedback, which enjoys global convergence. To simplify the structure of this three-layer distributed algorithm, a time-varying parameter-based two-layer inverse-free distributed algorithm is designed, which has global convergence. Moreover, to accelerate convergence and further simplify the structure of this two-layer distributed algorithm, we develop a Tikhonov-like regularization-based single-layer inverse-free distributed algorithm, which achieves consensus within finite time for any given initial point and possesses an O(1/ξ(t)) convergence rate of the linear-equality constraint function. Finally, experimental results on signal and image reconstruction are presented to illustrate the efficiency of our inverse-free distributed algorithms.