In this paper, we discuss the cone of copositive tensors and its approximation. We describe some basic properties of copositive tensors and positive semidefinite tensors. Specifically, we show that a non-positive tensor (or Z-tensor) is copositive if...
Large-scale neural networks have attracted much attention for surprising results in various cognitive tasks such as object detection and image classification. However, the large number of weight parameters in the complex networks can be problematic w...
Reconstructing images from multi-view projections is a crucial task both in the computer vision community and in the medical imaging community, and dynamic positron emission tomography (PET) is no exception. Unfortunately, image quality is inevitably...
Geometric iterative methods, including progressive iterative approximation and geometric interpolation methods, are efficient for fitting a given data set. With the development of big data technology, the number of fitting data points has become mass...
Synthetic aperture radar (SAR) images suffer from speckle noise due to their imaging mechanism, which deteriorates image interpretability and hinders subsequent tasks like target detection and recognition. Traditional denoising methods fall short of...
Hyperspectral image (HSI) possesses three intrinsic characteristics: the global correlation across spectral domain, the nonlocal self-similarity across spatial domain, and the local smooth structure across both spatial and spectral domains. This pape...
Noise removal is a fundamental problem in remote sensing image processing. Most existing methods, however, have not yet attained sufficient robustness in practice, due to more or less neglecting the intrinsic structures of remote sensing images and/o...
This paper presents a tensor approximation algorithm, based on the Levenberg–Marquardt method for the nonlinear least square problem, to decompose large-scale tensors into the sum of the products of vector groups of a given scale, or to obtain...
Recovering incomplete high-dimensional data to create complete and valuable datasets is the main focus of tensor completion research, which lies at the intersection of mathematics and information science. Researchers typically apply various linear an...
Low-rank tensors have received more attention in hyperspectral image (HSI) recovery. Minimizing the tensor nuclear norm, as a low-rank approximation method, often leads to modeling bias. To achieve an unbiased approximation and improve the robustness...
This work presents a novel approach to construct surrogate models of parametric differential algebraic equations based on a tensor representation of the solutions. The procedure consists of building simultaneously an approximation given in tensor-tra...
Tensor Robust Principal Component Analysis (TRPCA) plays a critical role in handling high multi-dimensional data sets, aiming to recover the low-rank and sparse components both accurately and efficiently. In this paper, different from current approac...
This paper presents a global and local tensor sparse approximation (GLTSA) model for removing the stripes in hyperspectral images (HSIs). HSIs can easily be degraded by unwanted stripes. Two intrinsic characteristics of the stripes are (1) global spa...
We introduce a tensor-product kind bivariate operator of a new generalization of Bernstein-type rational functions and its GBS (generalized Boolean sum) operator, and we investigate their approximation properties by obtaining their rates of convergen...
A hyperspectral image (HSI) contains abundant spatial and spectral information, but it is always corrupted by various noises, especially Gaussian noise. Global correlation (GC) across spectral domain and nonlocal self-similarity (NSS) across spatial...
The C-eigenpair of piezoelectric tensors finds applications in the area of the piezoelectric effect and converse piezoelectric effect. In this paper, we provide some characterizations of C-eigenvectors by exploring the structure of piezoelectric tens...
This paper is devoted to proposing a modified conjugate residual method for solving the generalized coupled Sylvester tensor equations. To further improve its convergence rate, we derive a preconditioned modified conjugate residual method based on th...
In this paper, we study the
This research article focuses on the method of vehicle crash velocity evaluation based on the tensor product approximation by B-splines. Weights associated with each observation are introduced in the least square method, which is based on probabilist...
Seismic data are easily contaminated by random noise, impairing subsequent geological interpretation tasks. Existing denoising methods like low-rank approximation (LRA) and deep learning (DL) show promising denoising capabilities but still have limit...
Infrared point-target detection is one of the key technologies in infrared guidance systems. Due to the long observation distance, the point target is often submerged in the background clutter and large noise in the process of atmospheric transmissio...
Condition monitoring and fault diagnosis are topics of growing interest for improving the reliability of modern industrial systems. As critical structural components, anti-friction bearings often operate under harsh conditions and are contributing fa...
We present examples of Padé approximations of the
To create a realistic 3D perception on glasses-free displays, it is critical to support continuous motion parallax, greater depths of field, and wider fields of view. A new type of Layered or Tensor light field 3D display has attracted greater attent...
Edge computing brings artificial intelligence algorithms and graphics processing units closer to data sources, making autonomy and energy-efficient processing vital for their design. Approximate computing has emerged as a popular strategy for energy-...
For system identification problems associated with long-length impulse responses, the recently developed decomposition-based technique that relies on a third-order tensor (TOT) framework represents a reliable choice. It is based on a combination of t...
Hyperspectral image compressive sensing reconstruction (HSI-CSR) is an important issue in remote sensing, and has recently been investigated increasingly by the sparsity prior based approaches. However, most of the available HSI-CSR methods consider...
The recently developed iterative Wiener filter using a fourth-order tensorial (FOT) decomposition owns appealing performance in the identification of long length impulse responses. It relies on the nearest Kronecker product representation (with parti...
We study the
In linear system identification problems, the Wiener filter represents a popular tool and stands as an important benchmark. Nevertheless, it faces significant challenges when identifying long-length impulse responses. In order to address the related...
This note is a short survey of nonnegative tensors, primarily from the geometric point of view. In addition to basic definitions, we discuss properties of and questions about nonnegative tensors, which may be of interest to geometers.
In this paper, we aim to develop an efficient algorithm for the solving Tensor Robust Principal Component Analysis (TRPCA) problem, which focuses on obtaining a low-rank approximation of a tensor by separating sparse and impulse noise. A common appro...
Tensor rank decomposition is a useful tool for geometric interpretation of the tensors in the canonical tensor model (CTM) of quantum gravity. In order to understand the stability of this interpretation, it is important to be able to estimate how man...
Graph-based multi-view clustering methods aim to explore the partition patterns by utilizing a similarity graph. However, many existing methods construct a consensus similarity graph based on the original multi-view space, which may result in the lac...
Tensor restoration finds applications in various fields, including data science, image processing, and machine learning, where the global low-rank property is a crucial prior. As the convex relaxation to the tensor rank function, the traditional tens...
Fiber orientation is an important descriptor of the microstructure for short fiber polymer composite materials where accurate and efficient prediction of the orientation state is crucial when evaluating the bulk thermo-mechanical response of the mate...
The paper presents k-version of the finite element method for boundary value problems (BVPs) and initial value problems (IVPs) in which global differentiability of approximations is always the result of the union of local approximations. The higher o...
Tensor product smoothers are frequently used to include interaction effects in multiple nonparametric regression models. Current implementations of tensor product smoothers either require using approximate penalties, such as those typically used in g...
In this paper, we extend the definition of tensor products from using an invertible matrix to utilising right-invertible matrices, exploring the algebraic properties of these new tensor products. Based on this novel definition, we define the concepts...
We have proposed the reduction in triple integral to double integral that is used in multiple shear mechanism model for faster 3D nonlinear ground motion analysis. In this study, we propose reformulation of the mechanism which results in the expressi...
This work focuses on linear system identification problems in the framework of the Wiener filter. Specifically, it addresses the challenging identification of systems characterized by impulse responses of long length, which poses significant difficul...
Existing tensor completion methods all require some hyperparameters. However, these hyperparameters determine the performance of each method, and it is difficult to tune them. In this paper, we propose a novel nonparametric tensor completion method,...
Since multi-view learning leverages complementary information from multiple feature sets to improve model performance, a tensor-based data fusion layer for neural networks, called Multi-View Data Tensor Fusion (MV-DTF), is used. It fuses M feature sp...
By means of Clifford Algebra, a unified language and tool to describe the rules of nature, this paper systematically discusses the dynamics and properties of spinor fields in curved space-time, such as the decomposition of the spinor connection, the...
In this article, a-Browder’s classical theorem is considered through the property
Interest in machine learning with tensor networks has been growing rapidly in recent years. We show that tensor-based methods developed for learning the governing equations of dynamical systems from data can, in the same way, be used for supervised l...
A long-standing issue in mathematical finance is the speed-up of option pricing, especially for multi-asset options. A recent study has proposed to use tensor train learning algorithms to speed up Fourier transform (FT)-based option pricing, utilizin...
We investigate the implications of different quantization approaches in Loop Quantum Cosmology for the primordial power spectrum of tensor modes. Specifically, we consider the hybrid and dressed metric approaches to derive the effective mass that gov...
Hyperspectral imaging is widely used to many applications as it includes both spatial and spectral distributions of a target scene. However, a compression, or a low multilinear rank approximation of hyperspectral imaging data, is required owing to th...
In recent years, the tensor completion algorithm has played a vital part in the reconstruction of missing elements within high-dimensional remote sensing image data. Due to the difficulty of tensor rank computation, scholars have proposed many substi...
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