Sparse Signal Recovery Based On Non-convex Optimization

Compressed Sensing(CS)is a new standard sampling theory proposed in recent years,which has a wide range of applications in signal processing,error correction,and wireless communication.The goal of compressed sensing is to hope to recover the original unknown sparse signal from fewer measured signals,through the observation matrix.The theoretical framework of compressive sensing is based on the sparsity of the signal and the reasonable choice of the observation matrix.For compressive perception,many in-depth explorations have been conducted by domestic and foreign scholars.Compressive sensing under convex optimization model has been widely studied.In this paper,based on the non-convex optimization model,the recovery of sparse signals under different conditions is investigated.1.For a signal with its own structural characteristics,its non-zero elements appear in blocks,and we call it a block sparse signal.Based on the block q-RIP condition,a sufficient condition for block sparse signal recovery is established by mixed l2/l_q norm minimization with q=2/3,and an error bound for signal recovery in the presence of noise case is obtained.Through numerical experiments,it is verified that the model has a high success rate for the recovery of block sparse signals.2.For the l_q(0<q?1)minimization model,a sufficient condition for sparse signal recovery is established by the cumulative coherence condition,and an error bound for signal recovery in the noisy case is obtained.