Related papers: Low-Rank Modeling and Its Applications in Image An…

Vision problems ranging from image clustering to motion segmentation to semi-supervised learning can naturally be framed as subspace segmentation problems, in which one aims to recover multiple low-dimensional subspaces from noisy and…

In this paper, we present and analyze a new set of low-rank recovery algorithms for linear inverse problems within the class of hard thresholding methods. We provide strategies on how to set up these algorithms via basic ingredients for…

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…

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…

The low-rank matrix completion problem can be succinctly stated as follows: given a subset of the entries of a matrix, find a low-rank matrix consistent with the observations. While several low-complexity algorithms for matrix completion…

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…

Deep learning has received extensive research interest in developing new medical image processing algorithms, and deep learning based models have been remarkably successful in a variety of medical imaging tasks to support disease detection…

Even in times of deep learning, low-rank approximations by factorizing a matrix into user and item latent factors continue to be a method of choice for collaborative filtering tasks due to their great performance. While deep learning based…

Dynamical low-rank algorithms are a class of numerical methods that compute low-rank approximations of dynamical systems. This is accomplished by projecting the dynamics onto a low-dimensional manifold and writing the solution directly in…

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…

In color image processing, image completion aims to restore missing entries from the incomplete observation image. Recently, great progress has been made in achieving completion by approximately solving the rank minimization problem. In…

Low-rank matrix completion consists of computing a matrix of minimal complexity that recovers a given set of observations as accurately as possible. Unfortunately, existing methods for matrix completion are heuristics that, while highly…

In this paper we consider the low-rank matrix completion problem with specific application to forecasting in time series analysis. Briefly, the low-rank matrix completion problem is the problem of imputing missing values of a matrix under a…

We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…

In this paper, we develop a nonconvex approach to the problem of low-rank and sparse matrix decomposition. In our nonconvex method, we replace the rank function and the $l_{0}$-norm of a given matrix with a non-convex fraction function on…

In this paper, the problem of matrix rank minimization under affine constraints is addressed. The state-of-the-art algorithms can recover matrices with a rank much less than what is sufficient for the uniqueness of the solution of this…

We study the problem of estimating low-rank matrices from linear measurements (a.k.a., matrix sensing) through nonconvex optimization. We propose an efficient stochastic variance reduced gradient descent algorithm to solve a nonconvex…

The common task in matrix completion (MC) and robust principle component analysis (RPCA) is to recover a low-rank matrix from a given data matrix. These problems gained great attention from various areas in applied sciences recently,…

In this paper, we propose a lower rank quaternion decomposition algorithm and apply it to color image inpainting. We introduce a concise form for the gradient of a real function in quaternion matrix variables. The optimality conditions of…

In recent years, large language models (LLMs) have driven advances in natural language processing. Still, their growing scale has increased the computational burden, necessitating a balance between efficiency and performance. Low-rank…