A smoothing neural network for minimization l1-lp in sparse signal reconstruction with measurement noises

This paper investigates a smoothing neural network (SNN) to solve a robust sparse signal reconstruction in compressed sensing (CS), where the objective function is nonsmooth l(1)-norm and the feasible set satisfies an inequality of l(p)-norm (2 >= p >= 1) which is used for measuring residual errors. With a smoothing approximate technique, the non-smooth and non-Lipschitz continuous issues of the l(1)-norm and the gradient of l(p)-norm can be solved efficiently. We propose a SNN which is modeled by a differential equation and give its circuit implementation. In this case, we prove the proposed SNN converges to the optimal of considered problem. Simulation results are discussed to demonstrate the efficiency of the proposed algorithm. (c) 2019 Elsevier Ltd. All rights reserved.