A smoothing neural network for minimization l₁-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 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 l₁-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.