Model Improvement And Algorithm Research Of Robust Principal Component Analysis In Image Processing

With the era of big-data coming,the human society has entered an era of "data-based survival",which can obtain massive and high dimensional data at all times.However,these high dimensional data are often redundant and contain noise in the field of computer vision,image processing,and signal processing.It has brought great obstacles to the storage,transmission and analysis of data.Therefore,it is necessary to reduce and denoise the massive high dimensional data.The robust principal component analysis(RPCA)is one of the mainstream methods of reducing dimension and denoising.This paper focus on the improvement of RPCA model and algorithm,and its application in image processing.The main work of this paper is as follows:First,in view of the practical application of image processing,the existing RPCA model and the original augmented Lagrange multiplier method are introduced.Then,the rank estimation is too large when the nuclear norm is used to approximate the rank function in original RPCA.To address this issue,a new non-convex approximation function,which combined with the properties of l?-norm and exponential functions,is proposed to approximate the rank function in the RPCA model.The new approximate model is solved by the augmented Lagrange multiplier method.This new model is applied to the background separation in image processing.The numerical experiment shows that the new non-convex approximation model is more efficient than the traditional convex approximation model.Next,the nuclear norm is widely used as a convex surrogate for the rank function in RPCA,which requires computing the singular value decomposition(SVD),a task that is increasingly costly as matrix sizes and ranks increase.To address this issue,we used robust bilinear factorization(RBF)to reduces the dimension of the matrix for which the SVD must be computed.At the same time,in view of the problem that the video sets often suffer from many challenges such as camouflage,lighting changes,and diverse types of image noise,the RPCA model is improved combined with motion map.In this paper,we propose a novel motion-assisted RPCA model with matrix factorization(FM-RPCA),and an efficient linear augmented lagrange multiplier method with matrix factorization(FL-ALM)algorithm is designed for the proposed new model.A large number of numerical experiments show that the improved model reduces the dimension of SVD,and it also improves the approximation efficiency.Moreover,a clearer video background can be obtained.Finally,the main content of this paper is summarized and the further research project is proposed based on some shortcomings of the existing models and algorithms.