Related papers: Leveraging Subspace Information for Low-Rank Matri…

Matrix sensing is the problem of reconstructing a low-rank matrix from a few linear measurements. In many applications such as collaborative filtering, the famous Netflix prize problem, and seismic data interpolation, there exists some…

Low-rank matrices play a fundamental role in modeling and computational methods for signal processing and machine learning. In many applications where low-rank matrices arise, these matrices cannot be fully sampled or directly observed, and…

Matrix recovery is the problem of recovering a low-rank matrix from a few linear measurements. Recently, this problem has gained a lot of attention as it is employed in many applications such as Netflix prize problem, seismic data…

In this paper, we study the problem of matrix recovery, which aims to restore a target matrix of authentic samples from grossly corrupted observations. Most of the existing methods, such as the well-known Robust Principal Component Analysis…

Low-rank modeling plays a pivotal role in signal processing and machine learning, with applications ranging from collaborative filtering, video surveillance, medical imaging, to dimensionality reduction and adaptive filtering. Many modern…

We propose and study a row-and-column affine measurement scheme for low-rank matrix recovery. Each measurement is a linear combination of elements in one row or one column of a matrix $X$. This setting arises naturally in applications from…

We consider the problem of estimation of a low-rank matrix from a limited number of noisy rank-one projections. In particular, we propose two fast, non-convex \emph{proper} algorithms for matrix recovery and support them with rigorous…

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…

For reconstruction of low-rank matrices from undersampled measurements, we develop an iterative algorithm based on least-squares estimation. While the algorithm can be used for any low-rank matrix, it is also capable of exploiting a-priori…

In this paper, we study first-order methods on a large variety of low-rank matrix optimization problems, whose solutions only live in a low dimensional eigenspace. Traditional first-order methods depend on the eigenvalue decomposition at…

We propose Matrix ALPS for recovering a sparse plus low-rank decomposition of a matrix given its corrupted and incomplete linear measurements. Our approach is a first-order projected gradient method over non-convex sets, and it exploits a…

Given the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, the goal of this paper is to establish deterministic conditions under which exact recovery of the low-rank and sparse…

We consider a problem of significant practical importance, namely, the reconstruction of a low-rank data matrix from a small subset of its entries. This problem appears in many areas such as collaborative filtering, computer vision and…

The goal of affine matrix rank minimization problem is to reconstruct a low-rank or approximately low-rank matrix under linear constraints. In general, this problem is combinatorial and NP-hard. In this paper, a nonconvex fraction function…

Recent theory of mapping an image into a structured low-rank Toeplitz or Hankel matrix has become an effective method to restore images. In this paper, we introduce a generalized structured low-rank algorithm to recover images from their…

We introduce a two step algorithm with theoretical guarantees to recover a jointly sparse and low-rank matrix from undersampled measurements of its columns. The algorithm first estimates the row subspace of the matrix using a set of common…

It has been recently shown that incorporating priori knowledge significantly improves the performance of basic compressive sensing based approaches. We have managed to successfully exploit this idea for recovering a matrix as a summation of…

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…

Low-rank modeling generally refers to a class of methods that solve problems by representing variables of interest as low-rank matrices. It has achieved great success in various fields including computer vision, data mining, signal…

We propose a method to reconstruct and cluster incomplete high-dimensional data lying in a union of low-dimensional subspaces. Exploring the sparse representation model, we jointly estimate the missing data while imposing the intrinsic…