Author Description

Front Cover -- Tensors for Data Processing -- Copyright -- Contents -- List of contributors -- Preface -- 1 Tensor decompositions: computations, applications, and challenges -- 1.1 Introduction -- 1.1.1 What is a tensor? -- 1.1.2 Why do we need tensors? -- 1.2 Tensor operations -- 1.2.1 Tensor notations -- 1.2.2 Matrix operators -- 1.2.3 Tensor transformations -- 1.2.4 Tensor products -- 1.2.5 Structural tensors -- 1.2.6 Summary -- 1.3 Tensor decompositions -- 1.3.1 Tucker decomposition -- 1.3.2 Canonical polyadic decomposition -- 1.3.3 Block term decomposition -- 1.3.4 Tensor singular value decomposition -- 1.3.5 Tensor network -- 1.3.5.1 Hierarchical Tucker decomposition -- 1.3.5.2 Tensor train decomposition -- 1.3.5.3 Tensor ring decomposition -- 1.3.5.4 Other variants -- 1.4 Tensor processing techniques -- 1.5 Challenges -- References -- 2 Transform-based tensor singular value decomposition in multidimensional image recovery -- 2.1 Introduction -- 2.2 Recent advances of the tensor singular value decomposition -- 2.2.1 Preliminaries and basic tensor notations -- 2.2.2 The t-SVD framework -- 2.2.3 Tensor nuclear norm and tensor recovery -- 2.2.4 Extensions -- 2.2.4.1 Nonconvex surrogates -- 2.2.4.2 Additional prior knowledge -- 2.2.4.3 Multiple directions and higher-order tensors -- 2.2.5 Summary -- 2.3 Transform-based t-SVD -- 2.3.1 Linear invertible transform-based t-SVD -- 2.3.2 Beyond invertibility and data adaptivity -- 2.4 Numerical experiments -- 2.4.1 Examples within the t-SVD framework -- 2.4.2 Examples of the transform-based t-SVD -- 2.5 Conclusions and new guidelines -- References -- 3 Partensor -- 3.1 Introduction -- 3.1.1 Related work -- 3.1.2 Notation -- 3.2 Tensor decomposition -- 3.2.1 Matrix least-squares problems -- 3.2.1.1 The unconstrained case -- 3.2.1.2 The nonnegative case -- 3.2.1.3 The orthogonal case.