Research On A Novel Robust Principal Component Analysis Model

With the continuous development of science and technology,especially with the popularization of online media,large-scale data analysis and processing technology play a more important role in life and scientific research.It is widely applied to many fields,such as image processing,signal processing,target identification,video analysis and so on.The increasing for people’s demands of information requires data with high integrity and accuracy.Due to the interference and pollution of external uncertain external factors and random factors,the accuracy of the final information declines.Therefore,it is crucial to recover the missing information data.The classical principal component analysis model is suitable for removing dense Gaussian small noise.However,denoising effect is not ideal and it lacks robustness in non-Gaussian noise or extremely large noise at some location.A robust principal component analysis model is proposed for the shortcomings of the principal component analysis model.The optimization problem of the robust principal component analysis model is solved by convex relaxation.The objective function is transformed into the problem of solving the kernel norm and l1 norm minimization.The robust principal component analysis model overcomes the noise-sensitive problem of the classical principal component analysis model.This model is robust for contained noise data.It has a wide range of applications and many mature solutions.In the practical image denoising problem,the picture is regarded as a matrix containing noise.The large singular values in the matrix can represent the main information of the data matrix.When using the robust principal component analysis model for image denoising,the kernel norm in the model assigns the same threshold of different singular values,and it does not consider the important meaning of the different structures represented by the singular values of the matrix.In addition,the l1 norm in the model does not consider the structure of the matrix itself,and has less effect on the noise recovery of a row(or a column)for data matrix.Therefore,the robust principal component analysis model is still not ideal for image denoising.Firstly,several robust models are intruduced in detail,including robust principal component analysis model,bilinear robust principal component analysis model,inductive robust principal component analysis model and orthonormal robust principal component analysis model.Secondly,in order to solve the problems existing in the robust principal component analysis model,a robust principal component analysis model is proposed based on weighted Schatten-p norm and l2,1norm.This model replaces the kernel norm with the weighted Schatten-p norm,which not only can make each different singular value of the matrix match the corresponding weights to prevent the main data information from losing too much,but also can accurately approximate the original low-rank matrix.Instead of the l1 norm,the l2,1 norm makes the model more robust to the structural information of the noise.Furthermore,based on the alternating direction multiplier method,an iterative solution algorithm is derived to solve the above models.Finally,this paper uses MATLAB to perform image denoising experiments,where model proposed in this paper is compared with the classical robust models.Through the experimental data and the effect of image denoising,the validity and feasibility of the proposed model can be analyzed for image denoising.