Study On Reconstruction Algorithms Of Compressed Sensing Based On Prior Information

As the booming development of modern scientific technology,people are in greater and greater need of information.The classic Nyquist sampling theory which traditional signal sampling process is based on requires high sampling rate,which highly increases the difficulty of the manufacturing of the sampling equipment.Sometimes it's even impossible to achieve it.In order to solve this problem,Donoho?Cand6s and Tao propose a brand new signal processing,Compressed Sensing(CS).The proposal of this theory enables the new procedure of first compressive sampling then transferring at a low rate.This leads to significant decrease of data sampling cost and reduction of storage.So CS is an innovation in the field of signal processing.The design of reconstruction algorithms has always been an important topic in the study of CS.Its performance has direct impact on the success of the application of CS theory.Current studies have proven that,appropriate use of the related prior information gathered in practical scenarios can greatly improve the quality of the reconstruction algorithms.Our study focuses on the recover schemes of CS based on different kinds of prior information.In this paper,we first briefly introduce the basic theory of CS and its development.Then we conclude and analyze some reconstruction algorithms of classic CS,for example convex optimization and greedy algorithms,and the scenarios with prior information in detail.Different scenarios leads to different kinds of prior information,among the most frequently used are partially known support,nonzero-probability model and sparsity structure.Because the algorithms proposed in this paper focus on block-sparse signals,we pay much attention on this kind of signal.To be followed,based on the partially known support,we use nonzero-probability model to present the continuous-nonzero character of block-sparse signals,so as to say,estimate the probability of each element in the form of power-law.In this way,we propose two algorithms based on block-sparse signals,Probability-Update Basis Pursuit(PU-BP)and PU Orthogonal Matching Pursuit(PU-OMP).In these two algorithms,the partially known support in PU-BP comes from prior knowledge.In comparison,PU-OMP exploits the selected support set from previous iterations as the prior partially known support of the present iteration,to update the probabilities of each entry.Noticing that in compressed spectrum sensing,the signals are block sparse,we experiment our algorithms in the background of it.Results show that,making full use of the continuous-nonzero property of block-sparse signals,our proposed algorithms have desirable reconstruction performance.What's more,it enjoys more advantage in dealing with signals of high sparsity rate.Last,we extend our algorithm to the scenario of Distributed CS(DCS).Based on the joint sparsity model(JSM)JSM-1,we modify the proposed PU-OMP to propose another algorithm,which refers to as PU-OMP-JSM-1.This algorithm makes full use of the inner block-sparsity and intra relations of the signals in the network.In this paper,we experiment it in the background of cooperative compressed spectrum sensing.Results further prove that,the proposed way to set the probability based on prior information can significantly improve the performance of reconstruction algorithms.