Research On High-Dimensional Image Denoising Via TT Rank

In the process of image generation and transmission,it is inevitable to be interfered by various noises,which affects the subsequent application of data.Therefore,the prob-lem of denoising derived from the actual demand has always been concerned.The method based on matrix factorization is widely used in existing studies.Although these methods can effectively remove noise interference,with the continuous expansion of data scale,they are faced with the problem of dramatically increasing the amount of calculation and even difficult to solve.Therefore,we need more stable and more robust models and algo-rithms to solve the problem of high-dimensional data denoising.Tensor Robust Principal Component Analysis(TRPCA)is committed to effectively recovering low-rank and s-parse components from observed high-dimensional data.The low-rank priori of tensors is an important basis for studying tensors,and the most commonly used method to charac-terize the low-rank tensor is to decompose it into several low-dimensional linear Spaces.At present,Tucker rank is commonly used to describe the low-rank property,which has good performance in dealing with common third-order tensor problems.However,when dealing with higher-order and larger tensors,the imbalance of expansion matrix and exponential increase of computation make these methods ineffectiv.In order to over-come this limitation,the global correlation of tensors is fully considered in this paper,and Tensor Train rank(TT rank)of tensor is introduced into the TRPCA problem to study the denoising model and algorithm.Firstly,TT rank is used as a low-rank constraint in the denoising model to achieve computability of higher-order tensors and better balance.Since direct rank minimization does not fully exploit the benefits of TT rank in addressing higher-order tensors,it is possible to improve the performance of our approach by trans-forming low-order tensors into higher-order tensors using a treatment of tensor enlarge-ment--Ket Augmentation(KA).For the sparsity of the noise component,the tensor l1norm is used as the sparsity constraint.Therefore,a TT rank based sparse and Gaussian mixture noise removal model is proposed,and the alternating direction multiplier algo-rithm(ADMM)is used to solve the model.Then,different noise levels are compared in three data types:color image,hyperspectral image and color video.Numerical results and visual effects show that the proposed model is superior to the tested methods,has good denoising performance.