Second order self-adaptive dynamical system for sparse signal reconstruction and applications to image recovery

In this article, we consider sparse signal reconstruction problems by an alternative second order self-adaptive dynamical system. By split feasibility problem of sparse signal reconstruction, we introduce a new second order self-adaptive dynamical system. Then, we prove that the proposed system has a unique solution under reasonable conditions. Furthermore, it is shown that the corresponding orbit of the system always converges. Finally, all kinds of numerical results on synthetic data and data from practical problems verify the efficiency of the proposed approach. © 2023 Elsevier Inc.