Improvement And Application Of Image Recovery Model Based On Low Rank Assumption

With the growing of image dimension,how to robustly recover an unknown image from the noisy observation images has become a challenging problem.The researchers found the latent low-dimensional structure in high-dimensional data and proposed different assumptions.Among them,the low-rank assumption employed the low-rank property of the real data itself,which has important research significance.As a result,the low-rank assumption based image recovery model has attracted extensive attention from scholars.As a classic image recovery model,the principal component analysis(PCA)method was widely used in dimensional reducing because of its fast calculation and excellent performance.PCA is sensitive to corruptions and outliers,because it employed the Frobenius norm to measure the reconstruction errors.In order to improve robustness,a variety of improved methods have been proposed.Among these methods,without using the past framework,the robust principal component analysis uses the low rank property of the real data and the sparseness of corruptions and outliers to build the model.This thesis focuses on the research of the low-rank assumption based robust principal component analysis,and offers the improvement and innovation of its drawbacks.First,we propose the robust principal component analysis based tri-decomposition model,which revealed the feasibility of decomposing one matrix into three component matrices for image recovery.Image recovery emerges in many areas,such as image processing,computer vision,and pattern recognition.Recently,the low-rank assumption based image recovery methods catch the researcher's attention.The basic assumption is that the real data matrix is low-rank and the error matrix is sparse.And,the assumption also demands that the low-rank component should be exactly low-rank,and the sparse component should be exactly sparse.However,either or both these assumptions cannot be exactly satisfied in practice and should be relaxed.To address this drawback,this thesis proposes a tri-decomposition model to dealing with the image data corrupted by both large sparse noise and small dense noise.The method divides the observed data into the clean data,sparse noise and dense noise.Extensive experiments on face images and surveillance videos demonstrate the effectiveness of the proposed method.Second,we propose masked robust principal component analysis,which aims to recover an unknown image matrix from noisy observations.Existing works,such as Robust Principal Component Analysis,are under the conditions that the image component and error component are additive,but in real world applications,the components are often non-additive.Especially an image may consist of a foreground object overlaid on the background,where each pixel either belongs to the foreground or the background.To separate image components robustly in such a situation,we employ a binary mask matrix which shows the location of sparse component and propose a novel image recovery model,called masked robust principal component analysis model.Meanwhile,we develop an iterative scheme based on inexact augmented Lagrange iterative method.Extensive experiments on face images and surveillance videos demonstrate the effectiveness of the proposed algorithm.