Related papers: Robust Low-Tubal-rank tensor recovery Using Discre…
Inspired by the row and column action methods for solving large-scale linear systems, in this work, we explore the use of frontal slices for solving tensor linear systems. In particular, this paper presents a novel approach for using…
Tensor time series, which is a time series consisting of tensorial observations, has become ubiquitous. It typically exhibits high dimensionality. One approach for dimension reduction is to use a factor model structure, in a form similar to…
Tensor completion can estimate missing values of a high-order data from its partially observed entries. Recent works show that low rank tensor ring approximation is one of the most powerful tools to solve tensor completion problem. However,…
Tactile perception is key to dexterous manipulation, yet simulating high-resolution elastomer deformation remains computationally prohibitive. Finite element methods (FEM) deliver high fidelity but demand costly remeshing, while Material…
Higher-order tensors arise frequently in applications such as neuroimaging, recommendation system, social network analysis, and psychological studies. We consider the problem of low-rank tensor estimation from possibly incomplete,…
Randomized iterative algorithms, such as the randomized Kaczmarz method and the randomized Gauss-Seidel method, have gained considerable popularity due to their efficacy in solving matrix-vector and matrix-matrix regression problems. Our…
This work proposes a hyper-reduction method for nonlinear parametric dynamical systems characterized by gradient fields such as Hamiltonian systems and gradient flows. The gradient structure is associated with conservation of invariants or…
Limited-angle electron tomography aims to reconstruct 3D shapes from 2D projections of Transmission Electron Microscopy (TEM) within a restricted range and number of tilting angles, but it suffers from the missing-wedge problem that causes…
We present an iterative method for the search of extreme entries in low-rank tensors which is based on a power iteration combined with a binary search. In this work we use the HT-format for low-rank tensors but other low-rank formats can be…
Mendelian randomization (MR) is a widely used tool for causal inference in the presence of unmeasured confounders, which uses single nucleotide polymorphisms (SNPs) as instrumental variables to estimate causal effects. However, SNPs often…
In this paper, we study multi-dimensional image recovery. Recently, transform-based tensor nuclear norm minimization methods are considered to capture low-rank tensor structures to recover third-order tensors in multi-dimensional image…
In this article we study the problem of signal recovery for group models. More precisely for a given set of groups, each containing a small subset of indices, and for given linear sketches of the true signal vector which is known to be…
Electrical impedance tomography is an imaging modality for extracting information on the conductivity distribution inside a physical body from boundary measurements of current and voltage. In many practical applications, it is a priori…
In this paper we propose a fast algorithm for trivariate interpolation, which is based on the partition of unity method for constructing a global interpolant by blending local radial basis function interpolants and using locally supported…
This paper introduces tensorial calculus techniques in the framework of Proper Orthogonal Decomposition (POD) to reduce the computational complexity of the reduced nonlinear terms. The resulting method, named tensorial POD, can be applied…
In previous work, theoretical analysis based on the tensor Restricted Isometry Property (t-RIP) established the robust recovery guarantees of a low-tubal-rank tensor. The obtained sufficient conditions depend strongly on the assumption that…
Tensor train (TT) factorization and corresponding TT rank, which can well express the low-rankness and mode correlations of higher-order tensors, have attracted much attention in recent years. However, TT factorization based methods are…
By exploiting the random sampling techniques, this paper derives an efficient randomized algorithm for computing a generalized CUR decomposition, which provides low-rank approximations of both matrices simultaneously in terms of some of…
The theory and computation of tensors with different tensor products play increasingly important roles in scientific computing and machine learning. Different products aim to preserve different algebraic properties from the matrix algebra,…
We present a new restricted SVD-based CUR (RSVD-CUR) factorization for matrix triplets $(A, B, G)$ that aims to extract meaningful information by providing a low-rank approximation of the three matrices using a subset of their rows and…