Tensor Rank Corrected Procedure For Image Restoration

With the rapid development of electronic and imaging technology,all aspects of our activities involve a large number of high-dimensional images,from color image,video data to medical images,hyper-spectral images,and face recognition,and fingerprint recognition with intelligent robot visual function.High-dimensional image has become an important form of multimedia,widely present in people's daily lives.How observational data from partial loss of recovering the original data has become a hot research field of image restoration problem.We know that most of the existing high-dimensional image and video data has a natural tensor structure,or can be organized into a tensor structure.Moreover,the tensor structure representation possesses good presentation skills and calculation features,thus on the basis of summarizing and inheriting the predecessors' research results.On the basis of the theory of tensor singular value decomposition(t-SVD),and tensor nuclear norm minimization model(TNN),This thesis has made some research of modeling,algorithm designing and algorithm analysis for low rank tensor recovery.The author's major contributions are outlined as follows:1.On concept of Fourier transform and tensor singular value decomposition,we propose tensor proximal point algorithm in the original domain for TNN model and give its convergence result.Numerical experiments for multi-linear images data completion show that tensor proximal point algorithm performs superior over ADMM.2.Based on the tensor nuclear norm minimization model and t-SVD,a tensor rank-correction model(CRTNN)is proposed to correct the tensor nuclear norm minimization model.A two-stage rank correction method is given as the following:the first stage is used to generate a pre-estimator by solving the TNN model,and the second stage is to solve the CRTNN model to generate a high-accuracy recovery by the pre-estimator.A tensor proximal point algorithm is proposed to solve the CRTNN model and the TNN model,making it possible to calculate tensor directly in the real field.Numerical experiments of medical images and video images verify the efficiency of the proposed model and method.The experimental results show that tensor rank-correction model and method can achieve higher-accuracy recovery.