Research On Tensor Robust Principal Component Algorithm

Vector and matrix,show obvious limitations in the processing of these high-dimensional data,and it is difficult to describe the complex structure of high-dimensional data accurately.Relatively speaking,tensor,as a natural generalization of vectors and matrices in high-dimensional space,has more advantages in analyzing and processing high-dimensional data.However,in fact,the obtained high-dimensional data usually has a lot of redundant information and noise,which not only increases the difficulty of data analysis and processing,but also greatly increases the complexity of data storage.In recent years,researchers have proposed many models and algorithms for low rank tensor robust principal component analysis.However,compared with vectors and matrices,the theory of tensor correlation is not very perfect.At present,the main problem of tensor robust principal component analysis is how to properly define the rank of tensor,which is different from the rank of matrix can be relaxed by kernel norm,but the rank of tensor is difficult to be defined,Therefore,a non-convex penalty function is constructed in this thesis,and the singular value of the tensor is applied to this function,so as to define a non-convex approximation of the rank of the tensor,which aims to characterize the rank of the tensor.Firstly,this thesis briefly introduces the research background,significance and research status of tensor robust principal component analysis.Secondly,the definitions,theorems and lemmas involved in this thesis are comprehensively explained,and the RPCA model,non-convex RPCA model,TRPCA model based on MCP function,TRPCA model based on SCAD-based are introduced in detail.Besides,this thesis proposes a rank-based non-convex approximation TRPCA model.Based on the singular value decomposition of tensor,this model characterized the rank of tensor by constructing a non-convex problem of non-convex penalty function.The parameterized non-convex penalty function is used to estimate the non-zero singular value more accurately than the kernel norm.Theoretically,it is proved that under certain assumptions,the global optimal solution of the objective function,namely the stability point,can be obtained.Experiments are carried out on actual image data,and the proposed method is compared with several common TRPCA algorithms.The experimental results show that the proposed algorithm is effective on image denoising both from subjective visual effects and objective criteria.