Dynamical Sparse Recovery With Finite-Time Convergence

Abstract

Even though sparse recovery (SR) has been successfully applied in a wide range of research communities, there still exists a barrier to real applications because of the inefficiency of the state-of-the-art algorithms. In this paper, we propose a dynamical approach to SR, which is highly efficient and with finite-time convergence property. First, instead of solving the $\ell _1$ regularized optimization programs that requires exhausting iterations, which is computer-oriented, the solution to SR problem in this paper is resolved through the evolution of a continuous dynamical system which can be realized by analog circuits. Moreover, the proposed dynamical system is proved to have the finite-time convergence property, and thus more efficient than locally competitive algorithm (LCA) (the recently developed dynamical system to solve SR) with exponential convergence property. Consequently, our proposed dynamical system is more appropriate than LCA to deal with the time-varying situations. Simulations are carried out to demonstrate the superior properties of our proposed system.