Research On Modeling And Algorithm Of High-dimensional Image Processing Based On Tensor Decomposition

As the sensor and computer hardware upgrade,high-dimensional images(e.g.,video,remotely sensed image,and magnetic resonance imaging)play an important role in our life and have been used in many applications,such as background extraction of video and hyperspectral target detection.However,it is necessary to reconstruct missing entries before these applications.On the one hand,missing entries would be introduced when acquiring the data by both/either the defective sensor and/or the poor atmospheric conditions.On the other hand,one can sample these high-dimensional images and store them in order to reduce the storage cost.In this work,we mainly focus on the reconstruction of these missing entries.As high-dimensional images are the natural tensor,we study the theories and applications of the tensor completion based on tensor decompositions.In detail,we study the potential prior knowledge of high-dimensional images and the practical applications of tensor completion.The main contents and contributions are as follows:We propose a non-convex approximation function for tensor Tucker-rank based on Tucker decomposition.Tensor Tucker-rank can characterize the low-rankness of each mode,i.e.,tensor Tucker-rank represents the correlation of each mode.Although the sum of nuclear norms(SNN)of unfolding matrices along each mode is the convex approximation,it does not take into consideration the practical meanings of different singular values.Based on the properties of logarithmic function,the proposed function shrinks the larger singular values less in order to preserve the major data components.We introduce this function into low-rank tensor completion and solve the proposed model using alternating direction method of multipliers(ADMM).Extensive experiments are given to demonstrate that the proposed method can significantly enhance the restoration quality on PSNR and SSIM values compared with the SNN-based methods,such as HaLRTC and ADMM-TR(E).Especially when the sampling rate is 10%,our method can reconstruct more details.Except for the Tucker decomposition,there are many other tensor decompositions,such as tensor singular value decomposition(t-SVD),which does not destroy the relationships between each mode.Based on t-SVD,we propose a non-convex thresholding function for tensor multi-rank.The key problem of the t-SVD based tensor completion methods is to study the practical meanings of singular tubes.We propose a non-convex approximate function for multi-rank in order to take into full consideration the practical meanings of different singular tubes.An ADMM-based method is proposed to solve this model.Extensive experiments about color images and video completion demonstrate that the proposed method recover better results in terms of PSNR and SSIM values than the SNN-and t-SVD-based methods.Tensor rank is a powerful tool for characterizing the relationships of each mode.However,there are many other priors for high-dimensional images.For instance,the data in spatial domain of video have piecewise smooth property.In this paper,we study the prior knowledge of factor matrices based on low-rank matrix factorization.In detail,we apply low-rank matrix factorization to the unfoldings along every mode.After studying the priors of factor matrices,we find that the piecewise smoothness of one factor matrix can preserve the spatial piecewise smoothness of original images.The proposed model not only considers the global correlation between the dimensions of the high-dimensional image,but also considers the spatial local smoothness of high-dimensional image.A block coordinate decent method is introduced to solve the proposed model.Extensive experiments illustrate that our method can significantly enhance the reconstruction quality on PSNR values and the relative error compared with the existing methods,such as HaLRTC and TMac.In addition,our method is more robust than TMac.There are many applications based on tensor decompositions.In this paper,we study to reconstruct the missing entries in multitemporal remotely sensed images(cloud and stripe removal).Missing information would be introduced when acquiring these data by both/either the defective sensor and/or the poor atmospheric conditions.The existing methods make use of only one or two kinds of relationships(spatial domain,spectral domain,or temporal domain).We propose a new methodology that makes full use of spatial,spectral,and temporal relationships for the reconstruction of missing data in multitemporal remotely sensed images.The proposed method considers the spatial nonlocal similarities by grouping similar patches,and reconstruct the missing data in the fourth dimensional group by low-rank tensor completion method that makes the best use of the global correlations in the spatial,spectral,and temporal domains.Experimental results on simulated and real data demonstrate that the proposed method is effective both qualitatively and quantitatively.