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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.…

Optimization and Control · Mathematics 2024-08-23 Quan Yu , Xinzhen Zhang

Affine rank minimization algorithms typically rely on calculating the gradient of a data error followed by a singular value decomposition at every iteration. Because these two steps are expensive, heuristic approximations are often used to…

Optimization and Control · Mathematics 2013-06-04 Stephen Becker , Volkan Cevher , Anastasios Kyrillidis

The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the least-square distance on the sampling set over…

Optimization and Control · Mathematics 2012-09-19 Bart Vandereycken

Low rank approximation is an important tool used in many applications of signal processing and machine learning. Recently, randomized sketching algorithms were proposed to effectively construct low rank approximations and obtain approximate…

Information Theory · Computer Science 2018-09-11 Shashanka Ubaru , Arya Mazumdar , Yousef Saad

Low-light image enhancement is a classical computer vision problem aiming to recover normal-exposure images from low-light images. However, convolutional neural networks commonly used in this field are good at sampling low-frequency local…

Computer Vision and Pattern Recognition · Computer Science 2022-09-19 Yunliang Zhuang , Zhuoran Zheng , Chen Lyu

The problem of low-rank matrix reconstruction arises in various applications in communications and signal processing. The state of the art research largely focuses on the recovery techniques that utilize affine maps satisfying the…

Signal Processing · Electrical Eng. & Systems 2020-04-07 Wei Zhang , Taejoon Kim , Guojun Xiong , Shu-Hung Leung

Iterative refinement is particularly popular for numerical solution of linear systems of equations. We extend it to Low Rank Approximation of a matrix (LRA) and observe close link of the resulting algorithm to oversampling techniques,…

Numerical Analysis · Mathematics 2024-11-28 Victor Y. Pan , Qi Luan , Soo Go

In this paper, we propose a new algorithm for recovery of low-rank matrices from compressed linear measurements. The underlying idea of this algorithm is to closely approximate the rank function with a smooth function of singular values,…

Information Theory · Computer Science 2016-11-18 Mohammadreza Malek-Mohammadi , Massoud Babaie-Zadeh , Mikael Skoglund

In this paper, we consider the challenge of reconstructing jointly sparse vectors from linear measurements. Firstly, we show that by utilizing the rank of the output data matrix we can reduce the problem to a full column rank case. This…

Numerical Analysis · Mathematics 2019-05-28 Armenak Petrosyan , Hoang Tran , Clayton Webster

In this paper we study the problem of recovering a low-rank matrix from a number of random linear measurements that are corrupted by outliers taking arbitrary values. We consider a nonsmooth nonconvex formulation of the problem, in which we…

Information Theory · Computer Science 2019-07-16 Xiao Li , Zhihui Zhu , Anthony Man-Cho So , Rene Vidal

The affine matrix rank minimization (AMRM) problem is to find a matrix of minimum rank that satisfies a given linear system constraint. It has many applications in some important areas such as control, recommender systems, matrix completion…

Optimization and Control · Mathematics 2018-11-26 Angang Cui , Jigen Peng , Haiyang Li , Junxiong Jia , Meng Wen

This paper presents a two-stage online algorithm for recovery of low-rank parameter matrix in non-stationary stochastic systems. The first stage applies the recursive least squares (RLS) estimator combined with its singular value…

Systems and Control · Electrical Eng. & Systems 2025-06-25 Yanxin Fu , Junbao Zhou , Yu Hu , Wenxiao Zhao

Recovery of low-rank matrices has recently seen significant activity in many areas of science and engineering, motivated by recent theoretical results for exact reconstruction guarantees and interesting practical applications. A number of…

Machine Learning · Statistics 2011-09-12 S. Derin Babacan , Martin Luessi , Rafael Molina , Aggelos K. Katsaggelos

Recent advances have shown that implicit bias of gradient descent on over-parameterized models enables the recovery of low-rank matrices from linear measurements, even with no prior knowledge on the intrinsic rank. In contrast, for robust…

Machine Learning · Computer Science 2020-06-17 Chong You , Zhihui Zhu , Qing Qu , Yi Ma

We consider the problem of recovering a lowrank matrix M from a small number of random linear measurements. A popular and useful example of this problem is matrix completion, in which the measurements reveal the values of a subset of the…

Information Theory · Computer Science 2009-10-05 Emmanuel J. Candes , Yaniv Plan

A matrix network is a family of matrices, with relatedness modeled by a weighted graph. We consider the task of completing a partially observed matrix network. We assume a novel sampling scheme where a fraction of matrices might be…

Machine Learning · Computer Science 2018-06-11 Qingyun Sun , Mengyuan Yan David Donoho , Stephen Boyd

Recovering a large matrix from limited measurements is a challenging task arising in many real applications, such as image inpainting, compressive sensing and medical imaging, and this kind of problems are mostly formulated as low-rank…

Computer Vision and Pattern Recognition · Computer Science 2014-06-12 Yilun Wang , Xinhua Su

Low-rank tensor estimation offers a powerful approach to addressing high-dimensional data challenges and can substantially improve solutions to ill-posed inverse problems, such as image reconstruction under noisy or undersampled conditions.…

Machine Learning · Computer Science 2025-02-06 Anh Van Nguyen , Diego Klabjan , Minseok Ryu , Kibaek Kim , Zichao Di

We propose a theory for matrix completion that goes beyond the low-rank structure commonly considered in the literature and applies to general matrices of low description complexity. Specifically, complexity of the sets of matrices…

Information Theory · Computer Science 2024-10-03 Erwin Riegler , Günther Koliander , David Stotz , Helmut Bölcskei

This paper considers theoretical analysis of recovering a low rank matrix given a few expansion coefficients with respect to any basis. The current approach generalizes the existing analysis for the low-rank matrix completion problem with…

Information Theory · Computer Science 2018-12-17 Abiy Tasissa , Rongjie Lai