Iterative Threshold Algorithm For Sparse Solutions To Linear And Nonlinear Constrained Problem

Due to the emerge of new signal processing theory “compressed sensing”,the study on sparse optimization theory has become research hot topic in image processing,signal processing and other fields.The class of regularized optimization problems has attracted much attention recently.Based on regularized optimization theory and the iterative threshold algorithm,this paper mainly discusses the algorithms to solve sparse optimization problem and their application to the signal processing.The main subjects of this paper include in the following three areas.Firstly,to overcome the default that the solution produced by the iterative algorithms is only approximate one,we take use of a simple real function extremum method,and deduce the expressions of exact solutions of the two kinds of special form of minimization problems.This ensures that the solutions obtained by the two types of minimization problems are accurate.Secondly,based on the ideology of iterative thresholding algorithm,as well as three special forms of threshold operators,with the use of the first order Taylor expansion,a class of the iterative thresholding operator algorithms(0 ? p ? 1)of the sparse solution of the linear systems are deduced and the theoretical convergence is given by fundamental calculus tools.And then,the new methods are used to the sparse signal recovery problems.The numerical results show that the new methods are faster and more efficient than the old ones.At last,combining with the iterative thresholding algorithms and the theory of linearization,iterative semi-threshold algorithm and iterative soft threshold algorithm for finding sparse solutions of nonlinear constrained problems are deduced,convergence analysis and a simple experiment of the new algorithm are given.