A second-order projection neurodynamic approach with exponential convergence for sparse signal reconstruction

Recently, a class of second-order neurodynamic approaches with convergence rates of O(1/t) or O(1/t(2)) has been developed to address the sparse signal reconstruction problem. In this paper, we propose a second-order projection neurodynamic approach (SOPNA) with exponential convergence to reconstruct a sparse signal by solving a modified inverted Gaussian function (MIGF) minimization problem. The existence, uniqueness, and feasibility of the solution to SOPNA are detailedly investigated, and the exponential convergence rate of O(exp(-mu t)),mu>0 is proved. This implies that our proposed SOPNA can achieve a significantly superior convergence performance than several existing second-order neurodynamic approaches. Numerical experiments also confirm its effectiveness and superiority. Finally, the applications of the proposed SOPNA in real signal and real image reconstructions validate its practical feasibility.