Research On Tseng’s Alternating Minimization Algorithm And Its Application

Many problems in signal and image processing,medical image reconstruction,and machine learning,among others,can be formulated as two-block separable convex minimization problems with linear equality constraints,one of which is strongly convex.The Tseng alternating minimization algorithm is one of the important algorithms for solving such problems.To improve the convergence speed of the algorithm,we propose a relaxed alternating minimization algorithm and prove that the proposed algorithm converges to the optimal primal-dual solution of the original problem.At the same time,the convergence rate of the proposed algorithm in the ergodic and nonergodic senses is investigated.We apply the proposed algorithm to solve several compound convex minimization problems that arise in image denoising and evaluate the numerical performance of the proposed algorithm on a new image denoising model.Numerical results on artificial and real noisy images verify the effectiveness and superiority of the proposed algorithm.The results obtained in this paper are as follows:First,we briefly introduce the research background,main research questions and the research status of this paper.Secondly,we introduce the preliminaries of this paper,including definitions,related lemmas,and conclusions.Then,we present a relaxed alternating minimization algorithm,and the convergence of the proposed algorithm and the rate of convergence in the ergodic and non-ergodic senses are also proved.Further apply the proposed algorithm to solve several complex convex minimization problems and point out connections to other existing algorithms.Next,a new image denoising model is proposed for Gaussian noise removal.Numerical experiments are conducted to verify the effectiveness and superiority of the proposed algorithm on both simulated and real-world noisy images.Finally,we present the conclusion and the outlook.