The Research Of Tensor Robust Principal Component Analysis Based On Truncated Nuclear Norm And Column/row Space Sampling

In recent years,with the rapid development and extensive application of computer technology,modern sensor and imaging techniques,people need to cope,analyse and recovery data with high dimension,large scale and sophisticated structure.In the process of data collecting and transmitting,these high dimensional data are inevitably influenced by random noises.How to explore the low-dimensional structure and recover original data from the observed data corrupted by noises has become hot spot research issues in the fields of computer vision,pattern recognition and data mining.However,traditional tensor decomposition and recovery algorithm did not consider the low-rank property and column/row space structure of tensor data,which leads to dissatisfactory effects in real application.Therefore,based on traditional tensor robust principal analysis,this thesis comes up with truncated singular value and tensor column/row space sampling algorithm to solve image denoising problem.The main contents of this thesis are summarized as follows:The first chapter briefly introduces the research background,significance and development of image denoising.Then the main research contents and organizational structure of this thesis are explained.The second chapter introduces some definitions and arithmetic about tensor,then gives the tensor incoherence conditions and other essential tensor recovery requirements based on tensor singular value decomposition,which provides relevant theoretical basis for subsequent chapters.The third chapter proposes tensor truncated nuclear norm denoising algorithm on the basis of traditional tensor robust principal analysis.This chapter then exhibits the low rank structure characteristic of tensor data.According to appropriately abandon smaller singular value,the denoising algorithm reduces computational complexity,improve recovery effects and this algorithm can be solved by alternating direction method of multipliers.The comparison between other denoising algorithms fully demonstrates the denoising effectiveness of the algorithm proposed in this chapter.The forth chapter proposes tensor decomposition algorithm based on column/row space sampling in order to solve the problem of long calculating time of traditional high dimensional tensor decomposition.According to sampling on column/row space respectively,this algorithm can reduce tensor dimension and convert original high dimensional tensor decomposition into two low dimensional subproblems.The proof of relevant theorems establishes a strict theoretical basis.Finally,the recovery and denoising experiments on synthetic data and real images demonstrate the superiority on time complexity dealing with high dimensional tensor.The fifth chapter summarizes the main works of this thesis,and looks forward to the future optimization and research on tensor denoising problem.