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Recent work in the matrix completion literature has shown that prior knowledge of a matrix's row and column spaces can be successfully incorporated into reconstruction programs to substantially benefit matrix recovery. This paper proposes a…

Information Theory · Computer Science 2025-09-10 Oscar López

We consider the problem of exact recovery of any $m\times n$ matrix of rank $\varrho$ from a small number of observed entries via the standard nuclear norm minimization framework. Such low-rank matrices have degrees of freedom $(m+n)\varrho…

Information Theory · Computer Science 2016-04-08 Abhisek Kundu

Expressing a matrix as the sum of a low-rank matrix plus a sparse matrix is a flexible model capturing global and local features in data popularized as Robust PCA (Candes et al., 2011; Chandrasekaran et al., 2009). Compressed sensing,…

Numerical Analysis · Mathematics 2022-04-28 Jared Tanner , Simon Vary

A matrix completion problem is to recover the missing entries in a partially observed matrix. Most of the existing matrix completion methods assume a low rank structure of the underlying complete matrix. In this paper, we introduce an…

Machine Learning · Statistics 2020-11-16 Chencheng Cai , Rong Chen , Han Xiao

Matrix completion (MC) is a promising technique which is able to recover an intact matrix with low-rank property from sub-sampled/incomplete data. Its application varies from computer vision, signal processing to wireless network, and…

Signal Processing · Electrical Eng. & Systems 2019-05-08 Xiao Peng Li , Lei Huang , Hing Cheung So , Bo Zhao

We present and analyze an efficient implementation of an iteratively reweighted least squares algorithm for recovering a matrix from a small number of linear measurements. The algorithm is designed for the simultaneous promotion of both a…

Numerical Analysis · Mathematics 2011-07-19 Massimo Fornasier , Holger Rauhut , Rachel Ward

In this survey, we provide a detailed review of recent advances in the recovery of continuous domain multidimensional signals from their few non-uniform (multichannel) measurements using structured low-rank matrix completion formulation.…

Computer Vision and Pattern Recognition · Computer Science 2020-02-19 Mathews Jacob , Merry P. Mani , Jong Chul Ye

Robust matrix completion (RMC) is a widely used machine learning tool that simultaneously tackles two critical issues in low-rank data analysis: missing data entries and extreme outliers. This paper proposes a novel scalable and learnable…

Machine Learning · Computer Science 2026-05-22 HanQin Cai , Chandra Kundu , Jialin Liu , Wotao Yin

We study the Riemannian optimization methods on the embedded manifold of low rank matrices for the problem of matrix completion, which is about recovering a low rank matrix from its partial entries. Assume $m$ entries of an $n\times n$ rank…

Numerical Analysis · Mathematics 2016-04-12 Ke Wei , Jian-Feng Cai , Tony F. Chan , Shingyu Leung

We describe the Simple Greedy Matrix Completion Algorithm providing an efficient method for restoration of low-rank matrices from incomplete corrupted entries. We provide numerical evidences that, even in the simplest implementation, the…

Numerical Analysis · Mathematics 2013-04-16 Alexander Petukhov , Inna Kozlov

Recovering a low rank matrix from a subset of its entries, some of which may be corrupted, is known as the robust matrix completion (RMC) problem. Existing RMC methods have several limitations: they require a relatively large number of…

Machine Learning · Computer Science 2025-12-16 Eilon Vaknin Laufer , Boaz Nadler

This paper studies the problem of recovering a signal vector and the corrupted noise vector from a collection of corrupted linear measurements through the solution of a l1 minimization, where the sensing matrix is a partial Fourier matrix…

Information Theory · Computer Science 2016-01-25 Dongcai Su

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

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…

Computer Vision and Pattern Recognition · Computer Science 2020-03-13 Pawan Goyal , Hussam Al Daas , Peter Benner

Previous work regarding low-rank matrix recovery has concentrated on the scenarios in which the matrix is noise-free and the measurements are corrupted by noise. However, in practical application, the matrix itself is usually perturbed by…

Information Theory · Computer Science 2020-03-09 Jianwen Huang , Jianjun Wang , Feng Zhang , Hailin Wang , Wendong Wang

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…

Information Theory · Computer Science 2016-12-12 Holger Rauhut , Ulrich Terstiege

In this paper, we theoretically investigate the low-rank matrix recovery problem in the context of the unconstrained regularized nuclear norm minimization (RNNM) framework. Our theoretical findings show that, the RNNM method is able to…

Numerical Analysis · Mathematics 2021-03-09 Wendong Wang , Feng Zhang , Jianjun Wang

We consider the problem of recovering a low-rank matrix when some of its entries, whose locations are not known a priori, are corrupted by errors of arbitrarily large magnitude. It has recently been shown that this problem can be solved…

Information Theory · Computer Science 2010-01-22 Arvind Ganesh , John Wright , Xiaodong Li , Emmanuel J. Candes , Yi Ma

We introduce a structured low rank matrix completion algorithm to recover a series of images from their under-sampled measurements, where the signal along the parameter dimension at every pixel is described by a linear combination of…

Computer Vision and Pattern Recognition · Computer Science 2017-07-13 Arvind Balachandrasekaran , Vincent Magnotta , Mathews Jacob

The recovery of the underlying low-rank structure of clean data corrupted with sparse noise/outliers is attracting increasing interest. However, in many low-level vision problems, the exact target rank of the underlying structure and the…

Computer Vision and Pattern Recognition · Computer Science 2020-10-29 Anyong Qin , Lina Xian , Yongliang Yang , Taiping Zhang , Yuan Yan Tang