Related papers: Alternating steepest descent methods for tensor co…

In the tensor completion problem, one seeks to estimate a low-rank tensor based on a random sample of revealed entries. In terms of the required sample size, earlier work revealed a large gap between estimation with unbounded computational…

This paper introduces an extended tensor decomposition (XTD) method for model reduction. The proposed method is based on a sparse non-separated enrichment to the conventional tensor decomposition, which is expected to improve the…

For solving pseudo-convex global optimization problems, we present a novel fully adaptive steepest descent method (or ASDM) without any hard-to-estimate parameters. For the step-size regulation in an $\varepsilon$-normalized direction, we…

Iterative methods based on tensors have emerged as powerful tools for solving tensor equations, and have significantly advanced across multiple disciplines. In this study, we propose two-step tensor-based iterative methods to solve the…

This paper examines the problem of state estimation in power distribution systems under low-observability conditions. The recently proposed constrained matrix completion method which combines the standard matrix completion method and power…

This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. Numerous renowned algorithms for tackling the compressed sensing problem…

We study extensions of compressive sensing and low rank matrix recovery (matrix completion) to the recovery of low rank tensors of higher order from a small number of linear measurements. While the theoretical understanding of low rank…

Tensor completion is an extension of matrix completion aimed at recovering a multiway data tensor by leveraging a given subset of its entries (observations) and the pattern of observation. The low-rank assumption is key in establishing a…

Low rank matrix and tensor completion problems are to recover the incomplete two and higher order data by using their low rank structures. The essential problem in the matrix and tensor completion problems is how to improve the efficiency.…

This study aims to solve the over-reliance on the rank estimation strategy in the standard tensor factorization-based tensor recovery and the problem of a large computational cost in the standard t-SVD-based tensor recovery. To this end, we…

In this paper we accomplish the development of the fast rank-adaptive solver for tensor-structured symmetric positive definite linear systems in higher dimensions. In [arXiv:1301.6068] this problem is approached by alternating minimization…

Due to the explosive growth of large-scale data sets, tensors have been a vital tool to analyze and process high-dimensional data. Different from the matrix case, tensor decomposition has been defined in various formats, which can be…

The advancement of sensing technology has driven the widespread application of high-dimensional data. However, issues such as missing entries during acquisition and transmission negatively impact the accuracy of subsequent tasks. Tensor…

The low multilinear rank approximation, also known as the truncated Tucker decomposition, has been extensively utilized in many applications that involve higher-order tensors. Popular methods for low multilinear rank approximation usually…

Higher-order low-rank tensors naturally arise in many applications including hyperspectral data recovery, video inpainting, seismic data recon- struction, and so on. We propose a new model to recover a low-rank tensor by simultaneously…

We study tensor completion (TC) through the lens of low-rank tensor decomposition (TD). Many TD algorithms use fast alternating minimization methods to solve highly structured linear regression problems at each step (e.g., for CP, Tucker,…

Recovering color images and videos from highly undersampled data is a fundamental and challenging task in face recognition and computer vision. By the multi-dimensional nature of color images and videos, in this paper, we propose a novel…

Tensor completion estimates missing components by exploiting the low-rank structure of multi-way data. The recently proposed methods based on tensor train (TT) and tensor ring (TR) show better performance in image recovery than classical…

We consider the problem of nonnegative tensor completion. We adopt the alternating optimization framework and solve each nonnegative matrix completion problem via a stochastic variation of the accelerated gradient algorithm. We…

In recent years, low-rank tensor completion (LRTC) has received considerable attention due to its applications in image/video inpainting, hyperspectral data recovery, etc. With different notions of tensor rank (e.g., CP, Tucker, tensor…