Image Denoising By Double Weighted Robust Principle Component Analysis

In the process of acquisition,transmission and storage,the image will inevitably be contami-nated by noise.In order to reduce the influence of noise on image analysis and processing,image needs to be denoised.How to remove the image noise signal and retain the image texture details as much as possible is always the key and difficult point in the field of noise reduction.In recent years,the low-rank matrix recovery theory extended by compressed sensing has made great progress,low-rank matrix recovery algorithm has also become one of the important methods to study image denoising.In this thesis,based on the typical algorithm of low-rank matrix recovery,the robust principal component analysis(RPCA)algorithm was used to denoising and verified by MATLAB simulation.The results in experiment show that although the classical RPCA algorithm can decrease the noise of the image by using the low-rank matrix as the raw representation of the noise-free image to be recovered,the image after denoising is relatively fuzzy and the texture is not clear enough due to some problems with the standard nuclear norm used in the recovery process of the low-rank matrix.In order to solve the defects of classical RPCA in image denoising,this thesis designs a double weighted RPCA denoising algorithm.When the traditional RPCA uses soft threshold to shrink the nuclear norm,the contraction degree is the same and the important matrix singular value prior information is ignored.Due to the importance of each of the singular value is different,the larger the singular values usually represent the main part of the image.Therefore,the weighted nuclear norm minimization algorithm is introduced into the RPCA model to construct the double weighted RPCA model with the double weighting of low-rank matrix and sparse matrix.The simulation experiment in MATLAB shows that the denoising effect of double weighted RPCA algorithm is improved compared with the existing denoising algorithm at different noise levels.In addition,compared with the classical RPCA algorithm,this algorithm not only retains the structure of the image,but also outperforms other noise algorithms in the maintenance of image detail texture.