Low Rank Image Restoration Research Based On Tensor RPCA Algorithm Via Matrix Norm

Low rank matrix recovery has become a hot topic in recent years.It has important applications in medical images,cultural relic images,monitoring videos,etc.A classic image restoration method is low-rank matrix restoration,which the main purpose is to recover the original matrix from the matrix containing destructive elements as much as possible.Low rank matrix restoration has achieved good results in low-rank gray image restoration.In this paper,the low-rank matrix restoration research is extended to the tensor level to discuss and the performance of tensor Robust Principal Component Analysis(RPCA)in gray image restoration is studied.The main work of this paper is as follows:The development status of traditional image restoration and low-rank image restoration is briefly described.For low rank image restoration,the traditional image restoration algorithms have the disadvantages of long repairing time and complex process.This paper discusses the typical optimization model based on low-rank matrix restoration and its corresponding solving algorithm,summarizes the advantages and disadvantages of the related algorithms.A tensor RPCA algorithm combining the matrix nuclear norm is proposed to solve the disadvantages of exist algorithms of long processing time and complexisity.A Tensor RPCA algorithm for low rank image denoising based on matrix norm is implemented,which is based on Tensor Singular Value Decomposition(t-SVD)of tensor Robust Principal Component Analysis(RPCA).Firstly,we get an f-diagonal tensor and two diagonal tensors through t-SVD decomposition.Then we get the matrix which is low rank from the f-diagonal tensor.It is observed that any frontal slice of the f-diagonal tensor is a diagonal matrix.Finally,on the basic of traditional tensor RPCA,we increase a solution of matrix nuclear norm while the original algorithm has a solution of tensor nuclear norm only.In this way,the low-rank components of tensors can be further extracted,Through experimental simulation and comparative analysis,it is concluded that the algorithm in this paper has advantages in processing image which the noise is sparser than the original one.When the interference contained in the damaged image is sparse enough,and the original image has a low-rank feature.This algorithm can be used for gray image restoration.Since tensor RPCA is used on the video repairing,we get the idea that the improved algorithm can be applied to low-rank gray image restoration.Therefore,first,we extend the corrupted grayscale images to a three dimensional space,which is named as the tensor level;Thereafter,we put forward the Tensor RPCA Algorithm via matrix norm to get low rank structure.Then we take low-rank tensor shrinking to matrix,the resulting matrix is the restored image.The improved algorithm is compared with the state-of-arts on gray image restoration algorithms for low rank image.The experiment results show that the proposed method has advantages in speed and efficiency.