Improvement And Application Of Nonconvex Low Rank Approximate Robust Principal Component Analysis Model

With the advent of the fourth technological revolution,the scale of data collection in many fields has shown an exponential growth.For example,in the field of image vision,due to the influence of the environment or image data collection tools,the collected data is often noisy,resulting in high-dimensional and large-scale data information.These noisy high-dimensional data pose a serious challenge to the processing and analysis of image video.In recent years,Robust Principal Component Analysis,as an important technology to remove data noise and extract outliers,has received widely followed from scholars at home and abroad.This paper mainly studies the improvement of robust principal component analysis model based on non-convex rank approximation and its application in image processing,high-dimensional data analysis and computer vision.The specific work is as follows:Firstly,the basic principles and model evolution of the robust principal component analysis model in the field of image processing are introduced,and several commonly used algorithms for solving the robust principal component analysis model are introduced.Secondly,for the problem that the kernel norm approximation rank function has too large rank estimation and high nuclear norm complexity,a new non-convex rank approximation function is proposed,which can more accurately approximate the real rank of the matrix.And satisfy the properties of the general matrix norm.An improved robust principal component analysis model is obtained based on the non-convex rank approximation function.The new model is solved by the augmented Lagrangian multiplier method.The numerical experiments of different real video data are used to verify that the new model is in static scene.The model calculation efficiency is fast and the separation effect is good.Thirdly,aiming at the problem that the existing low rank approximation model has poor processing effect and slow processing efficiency in dynamic background,the matrix bilinear decomposition characterization norm is introduced as the low rank term constraint,and the Markov random field model is used to overcome The effect of dynamic background pixels on foreground extraction yields a new robust principal component analysis model.The augmented Lagrangian multiplier method is used to solve the model.The numerical experiments show that the model has a great improvement in foreground extraction accuracy and computational efficiency compared with the traditional model.Finally,the main work of this paper is summarized and further research directions are proposed.