Related papers: Low-Rank Tensor Completion via Novel Sparsity-Indu…

For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation…

In this paper, we study the problem of image recovery from given partial (corrupted) observations. Recovering an image using a low-rank model has been an active research area in data analysis and machine learning. But often, images are not…

This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery…

This paper investigates a general class of problems in which a lower bounded smooth convex function incorporating $\ell_{0}$ and $\ell_{2,0}$ regularization is minimized over a box constraint. Although such problems arise frequently in…

This paper studies a recovery task of finding a low multilinear-rank tensor that fulfills some linear constraints in the general settings, which has many applications in computer vision and graphics. This problem is named as the low…

We consider the problem of recovering elements of a low-dimensional model from under-determined linear measurements. To perform recovery, we consider the minimization of a convex regularizer subject to a data fit constraint. Given a model,…

The topic of recovery of a structured model given a small number of linear observations has been well-studied in recent years. Examples include recovering sparse or group-sparse vectors, low-rank matrices, and the sum of sparse and low-rank…

This paper introduces a novel approach to learning sparsity-promoting regularizers for solving linear inverse problems. We develop a bilevel optimization framework to select an optimal synthesis operator, denoted as $B$, which regularizes…

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…

Modern decision-making scenarios often involve data that is both high-dimensional and rich in higher-order contextual information, where existing bandits algorithms fail to generate effective policies. In response, we propose in this paper…

The linear transform-based tensor nuclear norm (TNN) methods have recently obtained promising results for tensor completion. The main idea of this type of methods is exploiting the low-rank structure of frontal slices of the targeted tensor…

Sparse channel estimation for massive multiple-input multiple-output systems has drawn much attention in recent years. The required pilots are substantially reduced when the sparse channel state vectors can be reconstructed from a few…

Low rank tensor completion is a highly ill-posed inverse problem, particularly when the data model is not accurate, and some sort of regularization is required in order to solve it. In this article we focus on the calibration of the data…

In the present paper we propose two new algorithms of tensor completion for three-order tensors. The proposed methods consist in minimizing the average rank of the underlying tensor using its approximate function namely the tensor nuclear…

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…

Currently, existing tensor recovery methods fail to recognize the impact of tensor scale variations on their structural characteristics. Furthermore, existing studies face prohibitive computational costs when dealing with large-scale…

Low rank matrix recovery is the focus of many applications, but it is a NP-hard problem. A popular way to deal with this problem is to solve its convex relaxation, the nuclear norm regularized minimization problem (NRM), which includes…

We provide a rigorous analysis of implicit regularization in an overparametrized tensor factorization problem beyond the lazy training regime. For matrix factorization problems, this phenomenon has been studied in a number of works. A…

We consider the problem of noiseless and noisy low-rank tensor completion from a set of random linear measurements. In our derivations, we assume that the entries of the tensor belong to a finite field of arbitrary size and that…

Low-rank tensor completion (LRTC) aims to recover a complete low-rank tensor from incomplete observed tensor, attracting extensive attention in various practical applications such as image processing and computer vision. However, current…