Related papers: A Greedy Algorithm for Matrix Recovery with Subspa…
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…
Estimation of low-rank matrices is of significant interest in a range of contemporary applications. In this paper, we introduce a rank-one projection model for low-rank matrix recovery and propose a constrained nuclear norm minimization…
In this paper, we address the sparse multiple measurement vector (MMV) problem where the objective is to recover a set of sparse nonzero row vectors or indices of a signal matrix from incomplete measurements. Ideally, regardless of the…
In this work we address the problem of recovering sparse solutions to non linear inverse problems. We look at two variants of the basic problem, the synthesis prior problem when the solution is sparse and the analysis prior problem where…
We establish theoretical recovery guarantees of a family of Riemannian optimization algorithms for low rank matrix recovery, which is about recovering an $m\times n$ rank $r$ matrix from $p < mn$ number of linear measurements. The…
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…
Matrix recovery from sparse observations is an extensively studied topic emerging in various applications, such as recommendation system and signal processing, which includes the matrix completion and compressed sensing models as special…
Recovering brain connectivity from tract tracing data is an important computational problem in the neurosciences. Mesoscopic connectome reconstruction was previously formulated as a structured matrix regression problem (Harris et al.,…
Sparse recovery and subset selection are fundamental problems in varied communities, including signal processing, statistics and machine learning. Herein, we focus on an important greedy algorithm for these problems: Backward Stepwise…
Low rank model arises from a wide range of applications, including machine learning, signal processing, computer algebra, computer vision, and imaging science. Low rank matrix recovery is about reconstructing a low rank matrix from…
The restricted isometry property (RIP) is essential for the linear map to guarantee the successful recovery of low-rank matrices. The existing works show that the linear map generated by the measurement matrices with independent and…
Fourier domain structured low-rank matrix priors are emerging as powerful alternatives to traditional image recovery methods such as total variation and wavelet regularization. These priors specify that a convolutional structured matrix,…
We demonstrate a simple greedy algorithm that can reliably recover a d-dimensional vector v from incomplete and inaccurate measurements x. Here our measurement matrix is an N by d matrix with N much smaller than d. Our algorithm,…
This paper presents several novel theoretical results regarding the recovery of a low-rank matrix from just a few measurements consisting of linear combinations of the matrix entries. We show that properly constrained nuclear-norm…
Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…
We present a new, simple and computationally efficient iterative method for low rank matrix completion. Our method is inspired by the class of factorization-type iterative algorithms, but substantially differs from them in the way the…
The restricted isometry property (RIP) is a well-known condition that guarantees the absence of spurious local minima in low-rank matrix recovery problems with linear measurements. In this paper, we introduce a novel property named bound…
We investigate the problem of recovering a partially observed high-rank matrix whose columns obey a nonlinear structure such as a union of subspaces, an algebraic variety or grouped in clusters. The recovery problem is formulated as the…
The problem of finding the missing values of a matrix given a few of its entries, called matrix completion, has gathered a lot of attention in the recent years. Although the problem under the standard low rank assumption is NP-hard,…
The matrix recovery (completion) problem, a central problem in data science and theoretical computer science, is to recover a matrix $A$ from a relatively small sample of entries. While such a task is impossible in general, it has been…