Research On Image Restoration Optimization Algorithm Based On Total Variational Regularization And Matrix Completion

Images are widely used in modern society,but they are easy to degenerate under the influence of external factors,resulting in unnecessary waste of resources.Therefore,the research on the models and algorithms of image restoration has become one of the hot issues that many scholars pay close attention to.The total variation regularization method can effectively avoid the ill-conditioned problems in image restoration,and the matrix completion can effectively solve the problem of high-dimensional data.Therefore,the study of image restoration optimization algorithm based on total variation regularization and matrix completion have important theoretical and practical significance.In this dissertation,the optimization algorithm of image restoration based on total variation regularization method and matrix completion is studied systematically.Firstly,based on AFB algorithm of the total variation regularization model,a class of improve algorithm for updating the blurred image and bringing it into the iterative process is proposed according to the idea of replacing the abnormal points of the blurred image.Numerical experiments were carried out on AFB algorithm and the three most representative algorithms of this class improved algorithm,and five evaluation criteria are used to compare and analyze the restoration effects of these four algorithms.Secondly,for the problem that the three improved algorithms are not suitable for images with higher matrix dimensions,based on the theory of matrix completion can better process high-dimensional matrix images and the data points restored by the total variation regularization method can solve the problem that the constraint matrix of the matrix completion is difficult to determine,the idea of combining the matrix completion algorithm and the total variation regularization algorithm is proposed,and a new hybrid steepest descent algorithm is proposed for the following matrix completion model.The main work and conclusions of this paper are as follows:(1)In this numerical experiment,the restoration effect of the three improved algorithms is better than AFB algorithm,and three improved algorithms have stronger applicability.The three improved algorithms have relatively good restoration effect in different matrix dimensions,and have good restoration effect in head phantom image and abdomen phantom image.(2)A new restoration model is proposed based on the idea of replacing abnormal points in blurred images.That is,the adjustment variable is introduced,the single adjustment of the blurred image is transformed into the overall adjustment,and the solving algorithm of the improved model is given.(3)A hybrid alternating steepest descent method with higher computational efficiency and lower rank requirement is proposed.Aiming at the problem that the current alternating steepest descent algorithm used for matrix completion needs to know the matrix rank information in advance or the calculation efficiency is not high,combining the advantages of separate precise line search and two-stage algorithm,a new hybrid alternating steepest descent algorithm is proposed,and the convergence proof of the new algorithm is given.