Research On Tensor Modeling And Efficient Computation For High-Dimensional Image Processing

High-dimensional image data,including videos,hyperspectral images,and magnetic resonance images,plays an important role in real-world applications.However,owing to the limitation from the imaging environment,the imaging equipment,and the transmission condition,it is often necessary to face many inverse problems of high-dimensional images,i.e.,to estimate the high-dimensional data of high quality from the observed degraded data and the mechanism of the degradation.In this dissertation,we mainly focus on the tensor completion,the mixed noise removal from sensing hyperspectral images,and the video rain streaks removal.Solving these problems has important practical value in the high-dimensional image compression transmission,the outdoor computer intelligent vision system,and remote sensing applications.To tackle these problems,we mainly exploit the prior knowledge of observed high-dimensional data's inner-structure,i.e.,the global low-rankness,the local smoothness,and the non-local self-similarity.Based on the prior knowledge and the appropriate strategy of the disturbing term modeling,we propose the tensor regularization models,and design efficient and effective optimization algorithms to solve the models.The main novelties and contents are as follows:Firstly,based on the global low-rankness and the local piece-wise smoothness,which widely exist in high-dimensional image data,we propose a tensor completion model.We apply the low-rank matrix factorization along each mode of the tensor to enhance the overall low-rank property.Meanwhile,we regularize the sparsity of the coefficients of the factor matrix in the framelet domain,enhancing the spatial piece-wise smoothness.To efficiently solve the proposed model,we design an alternative inexact block coordinate descent algorithm.We prove that the proposed algorithm fits the block successive upper-bound minimization framework and its convergence is theoretically guaranteed.Under some mild conditions,our algorithm converges to the coordinate-wise minimum.Numerical experimental results on the videos,hyperspectral images,and magnetic resonance imaging data validate that the proposed method outperforms compared methods,such as TMac and a total variation based method.Secondly,we propose a hyperspectral image mixed noise removal method by fully utilizing the spectral global low-rankness and the spatial non-local self-similarity of the hyperspectral images.We adopt the low-rank subspace representation to constrain the global low-rankness along the spectral mode,and further formulate the fine denoising problem on the subspace representation coefficients.We enhance the spatial selfsimilarity by embedding a denoiser under the plug and play framework.Meanwhile,the mixed noise is modeled as a mixture of Gaussian.To solve the proposed regularization model,which is based on the maximum a posteriori estimation,we utilize the expectation maximization algorithm.Numerical experimental results show that the proposed method can effectively remove the mixed noise,of different types,in remote sensing hyperspectral images and adaptively estimate the statistical distribution of the noise.Thirdly,based on the overall low-rankness of the video data and the local directional property of the rain streaks,we proposed a tensor based video rain streaks removal model.In our model,we minimize the tensor nuclear norm of the video to boost its low-rankness and constraint several unidirectional total variation regularization terms to characterize the local directional property.We design an alternating direction method of multipliers based algorithm,the convergence of which is theoretically guaranteed,to solve the proposed model.Numerical experimental results on simulated data and real-world rainy videos demonstrate the effectiveness and efficiency of the proposed method.Fourthly,on the basis of the third part,we propose a fast video rain streaks removal method based on the local prior property in the gradient domain.The proposed model takes advantages of the local directionality of the rain streaks and the temporal continuity of the video,utilizing the discriminative prior knowledge between the clean video and rain streaks and It uses the prior information of the rain video,rain line and clean video with different degrees of discrimination in different directions.We develop a split augmented Lagrangian shrinkage algorithm,which is implemented on the graphics processing unit via the parallel programming.A large number of numerical experiments on simulated data and real-world rainy data verify that the proposed method outperforms compared methods.