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In this letter, we propose an algorithm for recovery of sparse and low rank components of matrices using an iterative method with adaptive thresholding. In each iteration, the low rank and sparse components are obtained using a thresholding…

Numerical Analysis · Computer Science 2017-04-13 Nematollah Zarmehi , Farokh Marvasti

We consider the recovery of a low rank and jointly sparse matrix from under sampled measurements of its columns. This problem is highly relevant in the recovery of dynamic MRI data with high spatio-temporal resolution, where each column of…

Numerical Analysis · Computer Science 2015-06-03 Sampurna Biswas , Sunrita Poddar , Soura Dasgupta , Raghuraman Mudumbai , Mathews Jacob

For a given matrix subspace, how can we find a basis that consists of low-rank matrices? This is a generalization of the sparse vector problem. It turns out that when the subspace is spanned by rank-1 matrices, the matrices can be obtained…

Numerical Analysis · Computer Science 2016-06-29 Yuji Nakatsukasa , Tasuku Soma , André Uschmajew

We propose an algorithmic framework, that employs active subspace techniques, for scalable global optimization of functions with low effective dimension (also referred to as low-rank functions). This proposal replaces the original…

Optimization and Control · Mathematics 2024-02-01 Coralia Cartis , Xinzhu Liang , Estelle Massart , Adilet Otemissov

In this paper we reformulate few-shot classification as a reconstruction problem in latent space. The ability of the network to reconstruct a query feature map from support features of a given class predicts membership of the query in that…

Computer Vision and Pattern Recognition · Computer Science 2021-04-28 Davis Wertheimer , Luming Tang , Bharath Hariharan

Image reconstruction from undersampled k-space data plays an important role in accelerating the acquisition of MR data, and a lot of deep learning-based methods have been exploited recently. Despite the achieved inspiring results, the…

Computer Vision and Pattern Recognition · Computer Science 2021-09-28 Chen Hu , Cheng Li , Haifeng Wang , Qiegen Liu , Hairong Zheng , Shanshan Wang

Image reconstruction based on an edge-sparsity assumption has become popular in recent years. Many methods of this type are capable of reconstructing nearly perfect edge-sparse images using limited data. In this paper, we present a method…

Image and Video Processing · Electrical Eng. & Systems 2019-02-04 Victor Churchill , Anne Gelb

We develop latent variable models for Bayesian learning based low-rank matrix completion and reconstruction from linear measurements. For under-determined systems, the developed methods are shown to reconstruct low-rank matrices when…

Machine Learning · Statistics 2015-01-26 Martin Sundin , Cristian R. Rojas , Magnus Jansson , Saikat Chatterjee

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

Variational formulations of reconstruction in computed tomography have the notable drawback of requiring repeated evaluations of both the forward Radon transform and either its adjoint or an approximate inverse transform which are…

Numerical Analysis · Mathematics 2017-05-23 Richard C. Barnard , Rick Archibald

Low-rank matrix factorizations arise in a wide variety of applications -- including recommendation systems, topic models, and source separation, to name just a few. In these and many other applications, it has been widely noted that by…

Machine Learning · Statistics 2016-11-01 Liangbei Xu , Mark A. Davenport

The problem of recovering a low-rank matrix from the linear constraints, known as affine matrix rank minimization problem, has been attracting extensive attention in recent years. In general, affine matrix rank minimization problem is a…

Optimization and Control · Mathematics 2020-01-31 Angang Cui , Jigen Peng , Haiyang Li

The task of recovering a low-rank matrix from its noisy linear measurements plays a central role in computational science. Smooth formulations of the problem often exhibit an undesirable phenomenon: the condition number, classically…

Optimization and Control · Mathematics 2019-04-24 Vasileios Charisopoulos , Yudong Chen , Damek Davis , Mateo Díaz , Lijun Ding , Dmitriy Drusvyatskiy

This paper introduces Laplace techniques for designing a neural network, with the goal of estimating simplex-constraint sparse vectors from compressed measurements. To this end, we recast the problem of MMSE estimation (w.r.t. a pre-defined…

Information Theory · Computer Science 2017-09-28 Steffen Limmer , Slawomir Stanczak

Matrix rank minimization (RM) problems recently gained extensive attention due to numerous applications in machine learning, system identification and graphical models. In RM problem, one aims to find the matrix with the lowest rank that…

Information Theory · Computer Science 2011-02-22 Amin Khajehnejad , Samet Oymak , Babak Hassibi

MRI is an inherently slow process, which leads to long scan time for high-resolution imaging. The speed of acquisition can be increased by ignoring parts of the data (undersampling). Consequently, this leads to the degradation of image…

Image and Video Processing · Electrical Eng. & Systems 2022-02-22 Soumick Chatterjee , Mario Breitkopf , Chompunuch Sarasaen , Hadya Yassin , Georg Rose , Andreas Nürnberger , Oliver Speck

We study a nonconvex optimization algorithmic approach to phase retrieval and the more general problem of semidefinite low-rank matrix sensing. Specifically, we analyze the nonconvex landscape of a quartic Burer-Monteiro factored…

Optimization and Control · Mathematics 2026-04-20 Andrew D. McRae

The low-complexity assumption in linear systems can often be expressed as rank deficiency in data matrices with generalized Hankel structure. This makes it possible to denoise the data by estimating the underlying structured low-rank…

Systems and Control · Electrical Eng. & Systems 2021-11-10 Mingzhou Yin , Roy S. Smith

The low-rank matrix approximation problems within a threshold are widely applied in information retrieval, image processing, background estimation of the video sequence problems and so on. This paper presents an adaptive randomized…

Numerical Analysis · Mathematics 2025-08-12 Qiaohua Liu , Yuejuan Yu

In this paper, we describe a low-rank matrix completion method based on matrix decomposition. An incomplete matrix is decomposed into submatrices which are filled with a proposed trimming step and then are recombined to form a low-rank…

Numerical Analysis · Mathematics 2010-06-29 Rick Ma , Samuel Cheng