Modeling And Algorithm For High-Order Data Processing Based On Tensor Low Rank Decomposition

With the development of computer technology and digital communication,high-order data are common in daily life and have become an important information carrier,such as color images,hyperspectral images,video,etc.Compared with one- or two-order data,high-order data contain information in multiple dimensions of data and is of high practical value in classification,medical diagnosis,object detection,face recognition,etc.Due to the limitations of imaging equipment,imaging conditions,etc.,the obtained high-order data are often incomplete or severely corrupted.This thesis focuses on two im-portant tasks in high-order data processing,i.e.,hyperspectral image super-resolution and video completion.Hyperspectral image super-resolution is a technique to obtain high spa-tial resolution hyperspectral images by fusing low spatial resolution hyperspectral images and high spatial resolution multispectral images in the same scene.Video completion refers to extrapolating unknown parts of the video from incomplete observations.Most of the proposed methods for hyperspectral image super-resolution and video completion are based on prior knowledge of the image,namely sparsity,smoothness,low rankness,etc.Higher-order images can be naturally modeled as low rank third-order tensors.In this thesis,we study high-order data processing models and algorithms based on low-rank tensors.Previous work on tensor singular value decomposition focused on the pursuit of lower rank in a single domain,while ignoring the potential in the cross-transform domain.The main contributions of this thesis are summarized as follows:1.We propose a novel tensor Cross-Domain rank for the task of hyperspectral im-age fusion based on a key observation,i.e.,the low-rank behavior in the defined Cross-Domain is more significant than that in single-domain.Specifically,we first define a successional linear transform to induct the so-called Cross-Domain,then develop a novel tensor Cross-Domain rank(CD-Rank),finally deduce a new tensor nuclear norm as its convex approximation mathematically.2.Equipped with the new tensor nuclear norm,we thus formulate a constrained CD-Rank minimization model,which could be effectively solved by alternating direction method of multipliers(ADMM).3.Extensive experiments on hyperspectral images and videos demonstrate the effec-tiveness of the proposed method.