Smoothing inertial projection neural network for minimization Lp−q in sparse signal reconstruction

In this paper, we investigate a more general sparse signal recovery minimization model and a smoothing neural network optimal method for compress sensing problem, where the objective function is a Lp−q minimization model which includes nonsmooth, nonconvex, and non-Lipschitz quasi-norm Lp norms 1≥p>0 and nonsmooth Lq norms 2≥p>1, and its feasible set is a closed convex subset of Rn. Firstly, under the restricted isometry property (RIP) condition, the uniqueness of solution for the minimization model with a given sparsity s is obtained through the theoretical analysis. With a mild condition, we get that the larger of the q, the more effective of the sparse recovery model under sensing matrix satisfies RIP conditions at fixed p. Secondly, using a smoothing approximate method, we propose the smoothing inertial projection neural network (SIPNN) algorithm for solving the proposed general model. Under certain conditions, the proposed algorithm can converge to a stationary point. Finally, convergence behavior and successful recover performance experiments and a comparison experiment confirm the effectiveness of the proposed SIPNN algorithm.