A smoothing neural network for minimization l 1 -l p 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 l1-norm and the feasible set satisfies an inequality of lp-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 l1-norm and the gradient of lp-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.