相关论文: Guaranteed Rank Minimization via Singular Value Pr…

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…

The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system…

We address the inverse problem that arises in compressed sensing of a low-rank matrix. Our approach is to pose the inverse problem as an approximation problem with a specified target rank of the solution. A simple search over the target…

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…

Affine matrix rank minimization problem is a fundamental problem with a lot of important applications in many fields. It is well known that this problem is combinatorial and NP-hard in general. In this paper, a continuous promoting low rank…

We develop an efficient stochastic variance reduced gradient descent algorithm to solve the affine rank minimization problem consists of finding a matrix of minimum rank from linear measurements. The proposed algorithm as a stochastic…

Singular value decomposition (SVD) and matrix inversion are ubiquitous in scientific computing. Both tasks are computationally demanding for large scale matrices. Existing algorithms can approximatively solve these problems with a given…

A classical problem in matrix computations is the efficient and reliable approximation of a given matrix by a matrix of lower rank. The truncated singular value decomposition (SVD) is known to provide the best such approximation for any…

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…

This paper describes a fast algorithm for recovering low-rank matrices from their linear measurements contaminated with Poisson noise: the Poisson noise Maximum Likelihood Singular Value thresholding (PMLSV) algorithm. We propose a convex…

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…

In this paper we revisit the sparse multiple measurement vector (MMV) problem where the aim is to recover a set of jointly sparse multichannel vectors from incomplete measurements. This problem has received increasing interest as an…

This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and…

Rank minimization can be converted into tractable surrogate problems, such as Nuclear Norm Minimization (NNM) and Weighted NNM (WNNM). The problems related to NNM, or WNNM, can be solved iteratively by applying a closed-form proximal…

In this paper, we study a general low-rank matrix recovery problem with linear measurements corrupted by some noise. The objective is to understand under what conditions on the restricted isometry property (RIP) of the problem local search…

The affine rank minimization (ARM) problem arises in many real-world applications. The goal is to recover a low-rank matrix from a small amount of noisy affine measurements. The original problem is NP-hard, and so directly solving the…

Recent work established that rank overparameterization eliminates spurious local minima in nonconvex low-rank matrix recovery under the restricted isometry property (RIP). But this does not fully explain the practical success of…

This paper is concerned with low-rank matrix optimization, which has found a wide range of applications in machine learning. This problem in the special case of matrix sensing has been studied extensively through the notion of Restricted…

The rank minimization problem is to find the lowest-rank matrix in a given set. Nuclear norm minimization has been proposed as an convex relaxation of rank minimization. Recht, Fazel, and Parrilo have shown that nuclear norm minimization…

Affine rank minimization problem is the generalized version of low rank matrix completion problem where linear combinations of the entries of a low rank matrix are observed and the matrix is estimated from these measurements. We propose a…