Study On Robust Matrix Completion Model Algorithms And Applications

Due to the advance of the technology of sensor,communication and computer,human beings could get massive data at all times.However,these data are often large scale,high dimensional,noises and missing,which brings difficulties and challenges such as data storage,transmission and analysis.Therefore,it is a hot topic to reduce the dimensionality and denoise in the field of information science,medicine and life science.The key technology of compressed sensing,the matrix completion,has attracted more attention in the fields of high dimensional data analysis,image processing and computer vision.This thesis focuses on the matrix completion model and its applications in image denoising.Thesis's main work is as follows:First of all,for the existing matrix completion model based on nuclear norm in solving the nuclear norm,the singular value decomposition is needed,and when the matrix dimension is too large to compute the complexity,the tri-factorization technique is introduced to decompose the original matrix into three smaller matrices,using the orthogonal invariance of the nuclear norm.The solution to the nuclear norm with higher dimensionality is transformed into the singular value decomposition of the nuclear norm with lower dimensionality,which greatly reduces the computational complexity.At the same time,the augmented Lagrangian multipliers method is used to solve the robust matrix completion model after dimensionality reduction.Finally,the improved model is applied to face recognition,and the feasibility and effectiveness of the algorithm are validated by experiments.Secondly,a new non-convex rank approximation function ?-norm is proposed for the problem that the traditional nuclear norm simply adds all the singular values and causes the large singular value to be excessively punished.Based on the non-convex rank approximation function,an improved non-convex matrix completion model is obtained and the augmented Lagrangian multipliers method is used to solve the non-convex model.Finally,the model is applied to the extraction of video background,the validity of the model and algorithm is validated by a lot of numerical experiments,and the ?-norm proposed in this chapter is a more accurate and robust approximation to the rank function.Finally,the main content of this paper is summarized and the further research project is proposed based on some shortcomings of the existing algorithms.