Related papers: Low rank tensor recovery via iterative hard thresh…

This paper presents a geometric analysis of the simultaneous blind deconvolution and phase retrieval (BDPR) problem via a structured low-rank tensor recovery framework. Due to the highly complicated structure of the associated sensing…

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…

This paper is concerned with the approximation of tensors using tree-based tensor formats, which are tensor networks whose graphs are dimension partition trees. We consider Hilbert tensor spaces of multivariate functions defined on a…

The task of reconstructing a low rank matrix from incomplete linear measurements arises in areas such as machine learning, quantum state tomography and in the phase retrieval problem. In this note, we study the particular setup that the…

We study the low-rank phase retrieval problem, where we try to recover a $d_1\times d_2$ low-rank matrix from a series of phaseless linear measurements. This is a fourth-order inverse problem, as we are trying to recover factors of matrix…

Compressed sensing is a paradigm within signal processing that provides the means for recovering structured signals from linear measurements in a highly efficient manner. Originally devised for the recovery of sparse signals, it has become…

This paper lies in the intersection of several fields: number theory, lattice theory, multilinear algebra, and scientific computing. We adapt existing solution algorithms for tensor eigenvalue problems to the tensor-train framework. As an…

The goal of tensor completion is to recover a tensor from a subset of its entries, often by exploiting its low-rank property. Among several useful definitions of tensor rank, the low-tubal-rank was shown to give a valuable characterization…

There are several different notions of "low rank" for tensors, associated to different formats. Among them, the Tensor Train (TT) format is particularly well suited for tensors of high order, as it circumvents the curse of dimensionality:…

The hierarchical SVD provides a quasi-best low rank approximation of high dimensional data in the hierarchical Tucker framework. Similar to the SVD for matrices, it provides a fundamental but expensive tool for tensor computations. In the…

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,…

In this paper, we consider the problem of compressed sensing where the goal is to recover almost all the sparse vectors using a small number of fixed linear measurements. For this problem, we propose a novel partial hard-thresholding…

In this paper, we propose a novel low-tubal-rank tensor recovery model, which directly constrains the tubal rank prior for effectively removing the mixed Gaussian and sparse noise in hyperspectral images. The constraints of tubal-rank and…

We consider the problem of learning low-rank tensors from partial observations with structural constraints, and propose a novel factorization of such tensors, which leads to a simpler optimization problem. The resulting problem is an…

Intensively growing approach in signal processing and acquisition, the Compressive Sensing approach, allows sparse signals to be recovered from small number of randomly acquired signal coefficients. This paper analyses some of the commonly…

We consider the problem of recovering a target matrix that is a superposition of low-rank and sparse components, from a small set of linear measurements. This problem arises in compressed sensing of structured high-dimensional signals such…

We study low rank approximation of tensors, focusing on the tensor train and Tucker decompositions, as well as approximations with tree tensor networks and more general tensor networks. For tensor train decomposition, we give a bicriteria…

In recent years, the application of tensors has become more widespread in fields that involve data analytics and numerical computation. Due to the explosive growth of data, low-rank tensor decompositions have become a powerful tool to…

Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit the tensor structure of function spaces and apply…

Randomized numerical linear algebra is proved to bridge theoretical advancements to offer scalable solutions for approximating tensor decomposition. This paper introduces fast randomized algorithms for solving the fixed Tucker-rank problem…