Time-varying neurodynamic optimization approaches with fixed-time convergence for sparse signal reconstruction

Abstract

Convergence speed is one of the most considerable features for sparse signal reconstruction algorithms. This paper introduces several novel fast time-varying neurodynamic optimization approaches (TVNOAs) with fixed-time convergence for sparse signal reconstruction. It is demonstrated that these trajectories converge to solutions within a fixed-time from arbitrary initial conditions, exhibiting a faster convergence rate due to the selection of appropriate time-varying coefficients. The fixed-time convergence of the proposed TVNOAs is investigated using the Polyak–Lojasiewicz condition. Moreover, explicit upper bounds for the settling time of TVNOAs are provided. Additionally, the robustness under bounded noises is further examined. Numerical experiments on sparse signal reconstruction validate the superiority of the proposed neurodynamic approaches.