A New Primal-dualalgorithm In Image Restoration Problems

Optimization is an important branch of operational research,and it plays an indispensable role in other disciplines.Many practical problems need to be converted into optimization problems with the help of mathematical ideas,seeking an optimal solution.In particular,in today's information age,Digital signal and image processing are also optimization problem that have been widely used.Therefore,it is very important to study an efficient optimization algorithm.This thesis systematically studies a new efficient algorithm by using the proximal point algorithm and primal-dual algorithm.The main research work and innovation are embodied as follows.For the convex optimization problem we studied,(?),we analyze the characteristics of existing algorithms,such as FBS,FISTA,PDHG,PPA,etc.Based on the PPA form of the PDHG algorithm,we know that its proximal matrix is asymmetric.This is not a standard PPA.Therefore,we improve the primal-dual algorithm by adopting a positive-definite and variate matrix as proximal matrix,and obtain a novel primal-dual algorithm.The new algorithm can be interpreted as a proximal point algorithm,hence the convergence can be derived under mild assumptions.The previous literature selects the parameter of step length more strictly,which greatly influences the efficiency of the algorithm.This thesis considers the requirement of step length for relaxation,and adopts an adaptive step length.Such a step length has a better selection range and a faster convergence speed.Preliminary experimental results show that when the new algorithm is applied to solve the image denoising problem,compared with some existing efficient algorithms,the new algorithm can get satisfactory results,and the calculation time is relatively short.