An Inertial Projection Neural Network for Sparse Signal Recovery via l1-αl2Minimization

Abstract

This paper aims to develop a new algorithm for recovering a sparse vector from a small number of measurements, which is a fundamental problem in the field of compressive sensing (CS). Currently, CS favors incoherent systems, in which any two measurements are as little correlated as possible. In reality, however, many problems are coherent, conventional methods such as 1 l minimization, do not work well. We propose a 1 2 l l −α minimization problem for compressed sensing using inertial projection neural network. The 1 2 l l −α minimization problem is presented for sparse signal recovery from highly coherent measurement matrices, differing from conventional 1 l minimization which uses standard convex relaxation. We describe in details how to incorporate inertial projection neural network into compressed sensing. Furthermore, numerical experiments are conducted to support the effectiveness and remarkable performance of the algorithm for sparse signal recovery.