Related papers: Tensor Arnoldi-Tikhonov and GMRES-type methods for…
In this paper, we define a semi-tensor product for third-order tensors. Based on this definition, we present a new type of tensor decomposition strategy and give the specific algorithm. This decomposition strategy actually generalizes the…
Tikhonov regularization is one of the most commonly used methods of regularization of ill-posed problems. In the setting of finite element solutions of elliptic partial differential control problems, Tikhonov regularization amounts to…
Solving linear discrete ill-posed problems for third order tensor equations based on a tensor t-product has attracted much attention. But when the data tensor is produced continuously, current algorithms are not time-saving. Here, we…
The T-product for third-order tensors has been used extensively in the literature. In this paper, we first introduce the first-order and second-order T-derivatives for the multi-vector real-valued function with the tensor T-product; and…
Many applications in science and engineering require the solution of large linear discrete ill-posed problems that are obtained by the discretization of a Fredholm integral equation of the first kind in several space-dimensions. The matrix…
Tensors of order three or higher have found applications in diverse fields, including image and signal processing, data mining, biomedical engineering and link analysis, to name a few. In many applications that involve for example time…
The numerical solution of linear discrete ill-posed problems typically requires regularization, i.e., replacement of the available ill-conditioned problem by a nearby better conditioned one. The most popular regularization methods for…
Model order reduction plays a crucial role in simplifying complex systems while preserving their essential dynamic characteristics, making it an invaluable tool in a wide range of applications, including robotic systems, signal processing,…
This paper derives the CS decomposition for orthogonal tensors (T-CSD) and the generalized singular value decomposition for two tensors (T-GSVD) via the T-product. The structures of the two decompositions are analyzed in detail and are…
The tensor Singular Value Decomposition (t-SVD) for third order tensors that was proposed by Kilmer and Martin~\cite{2011kilmer} has been applied successfully in many fields, such as computed tomography, facial recognition, and video…
In this paper, we will present a generalization of the L-tensor product (L-product) including generalization of the well known tensor cosine and T-products that were defined for third-order tensors and based on fast Fourier transform and…
We consider linear ill-conditioned operator equations in a Hilbert space setting. Motivated by the aggregation method, we consider approximate solutions constructed from linear combinations of Tikhonov regularization, which amounts to…
In the last decade, tensors have shown their potential as valuable tools for various tasks in numerical linear algebra. While most of the research has been focusing on how to compress a given tensor in order to maintain information as well…
We present a novel approach to nonlinear constrained Tikhonov regularization from the viewpoint of optimization theory. A second-order sufficient optimality condition is suggested as a nonlinearity condition to handle the nonlinearity of…
Higher-order tensors are becoming prevalent in many scientific areas such as computer vision, social network analysis, data mining and neuroscience. Traditional tensor decomposition approaches face three major challenges: model selecting,…
Randomized iterative algorithms, such as the randomized Kaczmarz method, have gained considerable popularity due to their efficacy in solving matrix-vector and matrix-matrix regression problems. Our present work leverages the insights…
Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the…
In this paper, we study the problem of a batch of linearly correlated image alignment, where the observed images are deformed by some unknown domain transformations, and corrupted by additive Gaussian noise and sparse noise simultaneously.…
Many inverse problems can be described by a PDE model with unknown parameters that need to be calibrated based on measurements related to its solution. This can be seen as a constrained minimization problem where one wishes to minimize the…
Recently, inverse problems have attracted more and more attention in computational mathematics and become increasingly important in engineering applications. After the discretization, many of inverse problems are reduced to linear systems.…