Related papers: Low-Rank Reduced Biquaternion Tensor Ring Decompos…
In this paper we develop two new Tensor Alternating Steepest Descent algorithms for tensor completion in the low-rank $\star_{M}$-product format, whereby we aim to reconstruct an entire low-rank tensor from a small number of measurements…
In color image processing, image completion aims to restore missing entries from the incomplete observation image. Recently, great progress has been made in achieving completion by approximately solving the rank minimization problem. In…
Tensor completion has emerged as a powerful framework for recovering missing data in multidimensional signals by exploiting low-rank tensor structures. Among existing approaches, linear transform-based tensor nuclear norm (TNN) methods have…
In recent years, quaternion matrix completion (QMC) based on low-rank regularization has been gradually used in image de-noising and de-blurring.Unlike low-rank matrix completion (LRMC) which handles RGB images by recovering each color…
Integrating a low-spatial-resolution hyperspectral image (LR-HSI) with a high-spatial-resolution multispectral image (HR-MSI) is recognized as a valid method for acquiring HR-HSI. Among the current fusion approaches, the tensor ring (TR)…
When the amount of entanglement in a quantum system is limited, the relevant dynamics of the system is restricted to a very small part of the state space. When restricted to this subspace the description of the system becomes efficient in…
The low-rank approximation is a complexity reduction technique to approximate a tensor or a matrix with a reduced rank, which has been applied to the simulation of high dimensional problems to reduce the memory required and computational…
The Tensor-Train (TT) format is a highly compact low-rank representation for high-dimensional tensors. TT is particularly useful when representing approximations to the solutions of certain types of parametrized partial differential…
Multispectral images contain many clues of surface characteristics of the objects, thus can be widely used in many computer vision tasks, e.g., recolorization and segmentation. However, due to the complex illumination and the geometry…
Tag-based image retrieval (TBIR) has drawn much attention in recent years due to the explosive amount of digital images and crowdsourcing tags. However, the TBIR applications still suffer from the deficient and inaccurate tags provided by…
This paper presents the reduced biquaternion mixed least squares and total least squares (RBMTLS) method for solving an overdetermined system $AX \approx B$ in the reduced biquaternion algebra. The RBMTLS method is suitable when matrix $B$…
Tensor completion is a fundamental tool for incomplete data analysis, where the goal is to predict missing entries from partial observations. However, existing methods often make the explicit or implicit assumption that the observed entries…
Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…
Tensor-based methods have recently emerged as a more natural and effective formulation to address many problems in hyperspectral imaging. In hyperspectral unmixing (HU), low-rank constraints on the abundance maps have been shown to act as a…
This paper proposes a theoretical framework to address the reduced biquaternion equality-constrained total least squares (RBTLSE) problem. The objective is to find an approximate solution to the system $AX \approx B$, subject to linear…
In this paper, we address the multi-view subspace clustering problem. Our method utilizes the circulant algebra for tensor, which is constructed by stacking the subspace representation matrices of different views and then rotating, to…
In this paper, a new definition of tensor p-shrinkage nuclear norm (p-TNN) is proposed based on tensor singular value decomposition (t-SVD). In particular, it can be proved that p-TNN is a better approximation of the tensor average rank…
The reduced-rank method exploits the distortion-variance tradeoff to yield superior solutions for classic problems in statistical signal processing such as parameter estimation and filtering. The central idea is to reduce the variance of…
Many applications in data science and scientific computing involve large-scale datasets that are expensive to store and compute with, but can be efficiently compressed and stored in an appropriate tensor format. In recent years, randomized…
Multi-relational learning has received lots of attention from researchers in various research communities. Most existing methods either suffer from superlinear per-iteration cost, or are sensitive to the given ranks. To address both issues,…