Research On The Application Of Low-rank Matrix Reconstruction Algorithm In Image

Images acquired are usually interfered by noise and destroying the detailed information,which can affect the further analysis.How to recover damaged images more accurately is still a difficult problem currently faced.Recently,the successful application of low-rank matrix theory in image reconstruction has widely concerned by researchers.This method achieves effective separation of noise by approximately decomposing the damaged image into the sum of the low-rank part and the sparse error part.This paper combines the current research progress of low-rank matrix restoration models to discuss the effect of low-rank matrix in the field of image restoration and analysis.The main researches are as follows:(1)Aiming at problem of insufficient robustness of face recognition methods to noise,make full use of the structural similarity between multiple faces,apply multi-matrix low-rank decomposition to face feature extraction,and explore low-rank subspace of face image sets Space,and then combined with the low-rank matrix recovery model to extract the low-rank features of the test sample.In addition,the PCA algorithm is used to further reduce the dimension of the extracted feature matrix,and the sparse representation classification method is used to test the effectiveness of feature extraction.When there is a certain amount of salt and pepper noise in the sample,the algorithm in this paper has better recognition accuracy on AR,Yale and CMU?PIE face databases.(2)On the basis of the structurally smooth reweighted low-rank matrix reconstruction model,a soft threshold low-rank matrix reconstruction algorithm based on block dicision were proposed.Firstly,the proposed method uses the idea of block division to improve the retention of local details;secondly,the weight parameters of the regularization items in the model are converted to soft thresholds,thereby improving the detail recovery effect of the model;finally,in order to solve the problem of weakening of edge information of the image by low-rank decomposition,the Laplacian sharpening operator is added in the iterative process of the algorithm,so as to realize the effective enhancement of the edge information.The improved algorithm proposed has an evident improvement influence in image restoration.(3)Aiming at the problem that the low-rank matrix restoration model of the first-order TV regularization is prone to a staircase effect in the application of image restoration,this paper makes full use of the advantages of the high-order TV regularization term and integrates it into the low-rank matrix restoration model,and proposes the reweighted low-rank matrix reconstruction model of high-order TV regularization,and constructs an algorithm for solving optimization model based on the alternating direction multiplier method.The experimental results show that the optimization model proposed in this paper has better performance in image restoration.