Low Rank Matrix Triple Decompositions And Application

With the development of information technology,large-scale data is all the time,everywhere.This brings opportunities and challenges to the development of computer vision,pattern recognition,data mining,and machine learning.Low rank matrix decomposition is a commonly used data analysis tool to solve these problems.In the process of image acquisition or processing,it is often disturbed by various noises.How to recover the real image from the images with noise is particularly important.This thesis mainly decomposes the matrix into the sum of three matrices.Firstly,this thesis expounds the existing models:principal component analysis,robust principal component analysis and double nuclear matrix decomposition.The ideas,principles,solution methods and applications of the above three models are discussed,and the advantages and disadvantages of each model are summarized.Secondly,in order to enhance the robustness of the matrix decomposition model,a robust matrix decomposition method based on double nuclear norm is proposed.This method can be used to recover the image data corrupted by continuous occlusion.This method decomposes each data matrix into the sum of low-rank clean data,low-rank noise data and sparse noise data.An optimization model is established to minimize the weighted combination of double nuclear norm and L₁ norm of the matrix and an alternating direction method of multipliers is presented to solve it.Experimental results on real data sets verify the feasibility and effectiveness of the proposed method.Finally,based on the double nuclear robust matrix decomposition algorithm,the low rank clean matrix is decomposed into two matrix product forms by using two new norms:S_1/2norm and S_2/3 norm.Two new models proposed,double nuclear double nuclear robust matrix decomposition and the Frobenius nuclear double nuclear robust matrix decomposition is proposed.The good performance of the algorithm is verified from both quantitative analysis and visual effects.