The Tensor Completion Under Poisson Noise

In recent years,with the rapid development of information technology,high-dimensional images as an information carrier play an increasingly important role.High-dimensional images have indispensable important application in many fields,such as technology,military,and commerce.However,in the process of acquisition and transmission,high-dimensional images inevitably have some information missed and damaged.Therefore,in the field of image processing and computer vision,high-dimensional images completion and denoising is a very important research topic.Traditional methods often deal with image completion and denoising problems separately.This paper mainly studies the combination of image information lost and damage,which is to study the high-dimensional image restoration problem that combines the completion with denoising problems.The main research contents of this paper are as follows:A high-dimensional image is usually mathematically recorded as a high-dimensional array,which is a tensor.Since the definition of tensor rank is not unique,this paper mainly uses matrix rank,tensor Tucker rank,and tensor Tubal rank to establish the corresponding image restoration model.Since the rank minimization problem of tensors is an NP-hard problem,this requires us to find a convex relaxation of the rank to approximate the exact rank.Therefore,according to the different definitions of rank,we derive MNN,SNN and TNN as the convex approximation of matrix rank,Tucker rank,and Tubal rank,respectively.At the same time,the noise distribution is an important prior knowledge,so we analyze the performance properties of the loss function under Poisson noise and its properties.Based on the above analysis,we have established three tensor restoration regularization models under Poisson noise,namely matrix rank based model,tensor Tucker rank based model,and tensor Tubal rank based model,in which the loss function is fidelity term and the constraint of low rank is regular term.In order to solve the proposed models,we design three algorithms based on alternating direction multiplier method(ADMM)and analyze the convergence of the algorithm.We chose structural color image,random low-rank tensor and multispectral image for experiment with different sampling rates.Using PSNR and SSIM as the evaluation indexes,we have obtained the conclusion: among the three models,the low rank tensor restoration modelbased on SNN is superior to the other two models,which is more observably in random low-rank tensor and multispectral image and a little difference in color image.Finally,for the multispectral image,a twist tensor TNN repair method is proposed,which makes the recovery result significantly improved.