Research On Sparse Optimization Algorithm

Compressed sensing is a sampling theory based on signal sparsity.It is an important means in the digital age.It is widely used in the fields of compression imaging,astronomy,radar imaging,communication,medical images and so on.The reconstruction algorithm is the key to the application of compressed sensing in reality,so finding an effective sparse optimization algorithm becomes the top priority of solving the problem.This paper mainly focuses on the reconstruction of compressed sensing signal,combining the original dual interior point algorithm,linear Bregman iterative algorithm,truncated Newton interior point algorithm and improved differential evolution algorithm to solve the minimum l1 norm problem.The main research work of this paper is as follows:(1)On the basis of describing the background,significance and current research situation of compressed sensing,the research status and significance of sparse optimization algorithm are emphasized.(2)In this paper,the differential evolution algorithm in intelligent algorithm is mainly studied,and on this basis,an improved differential evolution algorithm is proposed,which is applied to the solution of the problem of compressed sensing.The method is used to show that the norm has a better sparse solution,and further illustrates the improved differential evolution algorithm when the variable is less.It has good effect in signal reconstruction.(3)Several classical convex optimization algorithms are compared,that is,the original dual interior point method,the linear Bregman iteration algorithm and the truncated Newton interior point method,and give the numerical simulation.The results show that the original dual interior point algorithm has better reconstruction effect.(4)The selection of regularization parameters is studied and analyzed.The selection of regularization parameters of the truncated Newton interior point method is emphatically studied.Numerical simulation shows that there is a relatively good reconstruction effect when the selection of regularization parameters is appropriate.