Research On Compressed Sensing Theory And Application

There are some limitations of the traditional sampling method,while compressed sensing theory saves the resources of collecting redundant information by compressing while sampling,which greatly reduces the pressure of signal storage and transmission,therefore,it has been considered as one of the important technologies in the field of signal processing.In this study,on the basis of the three directions of the compressed sensing theory: The selection of sparse bases,the design of the observation matrix,and the optimization of the reconstruction algorithm.The main work is as follows:(1)In this paper,the basic framework of compressed sensing theory has been described systematically.Subsequently,from three elements of the theory,the sparse signal representation,observation matrix and reconstruction algorithm commonly employed have been illustrated respectively.In addition,their advantages and disadvantages are compared and analyzed.(2)Moreover,the finite isometric property and its approximate equivalence conditions are introduced in detail.Based on the advantages and disadvantages of commonly used observation matrices,and taking the column coherence of the matrix as a reference criterion,a new observation matrix has been proposed creatively.Subsequently,the common observation matrices are compared by one-dimensional signal and two-dimensional image simulation experiments.Notably,the experimental results have verified the superiority of the new observation matrix,with reflecting the value of the observation matrix as an intermediate bridge simultaneously.(3)In order to solve the standard difference between Co Sa MP algorithm in selecting and eliminating atomic basis in the iterative process,an improved algorithm,u Co Sa MP algorithm has been proposed.In the atom selection stage,the correction matrix adaptively corrects the correlation between the residual and the observation matrix,which has been adopted by the algorithm to improve the accuracy of the candidate set.While in the atom elimination stage,it is divided into two steps.First,the least square method has been adopted to reduce the size of the candidate set to 2K.Second,by employing the weighted sum of signals and residuals,the final support set has been obtained,in addition,the superior reconstruction performance of the algorithm has been verified and improved by several simulation experiments.Finally,combining theory with practice,compressed sensing theory has been applied to the locust plague monitoring system,which is intended to produce the practical value of this research.