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

•By split feasibility problem of sparse signal reconstruction, we introduce a new second order self-adaptive dynamical system and the existence and uniqueness of strong global solutions of the second order dynamical system are revealed.•The convergence of the trajectories is established under milder conditions, which presents a theory guarantee for its applications.•To show the efficiency the proposed algorithm, all kinds of numerical experiments including large scale examples are raised on signal processing and image restoration to verify the superior efficiency of the proposed algorithm.