A Smoothing Inertial Neural Network for Sparse Signal Reconstruction with Noise Measurements via Lp-L1 minimization

Lieqin Jiang, Xing He

Abstract: In this paper, a smoothing inertial neural network (SINN) is proposed for the $$L_{p}$$ L p - $$L_{1}$$ L 1 $$(1\ge p>0)$$ ( 1 ≥ p > 0 ) minimization problem, in which the objective function is non-smooth, non-convex, and non-Lipschitz. First, based on the smooth approximation technique, the objective function can be transformed into a smooth optimization problem, effectively solving the $$L_{p}$$ L p - $$L_{1}$$ L 1 $$(1\ge p>0)$$ ( 1 ≥ p > 0 ) minimization model with non-smooth terms. Second, the Lipschitz property of the gradient that is smooth objective function is discussed. Then through theoretical analysis, the existence and uniqueness of the solution is discussed under the condition of restricted isometric property (RIP), and it is proved that the proposed SINN converges to the optimal solution of the minimization problem. Finally, the effectiveness and superiority of the proposed SINN are verified by the successful recovery performance under different pulse noise levels.