Localized Low-Rank Promoting For Image Denoising Based On Robust Principal Component Analysis Method

With the rapid development of computer information processing technology and the widespread popularization of the Internet industry,the increasingly rich data is often mixed with various forms of noise pollution,which reduces the accura-cy and integrity of information.How to denoise the contaminated image and keep the original details and important features of the data has always been a hot topic in the academic field.In recent years,with the expansion of algorithms and the-ories,Robust Principle Component Analysis(RPCA)has brought a breakthrough in the field of image processing.This method aims to recover the low-dimensional structure of the data matrix from the real observation matrix with the premise of modelling the corrupted noise parts with arbitrary distribution and magnitude as a sparse matrix.In this paper,we proposes a novel optimization program for solving the RPCA problem,which decomposes a data matrix into a conventional low-rank part plus a particular block-sparse residual.Different from most currently existing approaches,the study perceived especially a highly spatial correlation among the inner structure of the neighbouring pixels in this contiguously block-sparse residu-al.Typically,a method named Localized low rank Promoting(LOOP)is introduced with a theoretical guarantee for recovery of the intra-block correlation problem.The main contents are as follows:The first chapter briefly summarizes the background and research significance of image denoising,analyzes the existing image denoising techniques,and summarizes the main work and the organization structure of this paper.In the second chapter,the mathematical notation and matrix algebra are sum-marized and explained,and the basic theories of Compressive Sensing(CS)and Ro-bust Principle Component Analysis(RPCA)are reviewed.Then,the classical block sparse signal recovery model is introduced,and the new optimization problem for decomposing an observation matrix into a low-rank part plus a block-sparse residual are further discussed.In the third chapter,a new approach of low-rank and block-sparse decompo-sition motivated by the LOOP method,named RPCA-LOOP,is proposed with a theoretical guarantee.The high intra-block correlation is introduced as prior infor-mation to deal the new governing optimization problem.In order to solve this convex minimization program,an efficient solving algorithm is designed accordingly with a theoretical convergence analysis by adopting the classical Alternating Direction Method of Multipliers(ADMM)framework.In the fourth chapter,a series of synthetic simulations together with a real application on image denoising experiment have been conducted to demonstrate the superiority of the proposed RPCA-LOOP method.As expected,the simulation experiments verify our model is more effffective and highly competitive for outlier detection.Even when applied to practical applications of image denoising,there still are evident advantages.The fifth chapter summarise the main work of the paper,and the future theo-retical research and practical application are analyzed and prospected.