Neurodynamic optimization algorithm for split equality problems and application to sparse signal recovery

Abstract

In this paper, we propose a fixed-time neurodynamic optimization algorithm with time-varying coefficients (TFxND) for solving split equality problems. Under bounded linear regularity condition, we prove that the proposed neurodynamic algorithm converges to a solution of the split equality problem in fixed-time, which is independent of the initial states. In addition, the proposed TFxND is applied to solve the sparse signal recovery and sparse image reconstruction. The effectiveness and superiority of the proposed approach are illustrated through numerical experiments, which compare it favorably against other methods. Specifically, compared with the existing state-of-the-art sparse image reconstruction algorithm with fixed-time convergence, our proposed method achieves a 2.94 times speedup while maintaining equivalent reconstruction quality.