Related papers: Relaxed Leverage Sampling for Low-rank Matrix Comp…
Recovering sparse vectors and low-rank matrices from noisy linear measurements has been the focus of much recent research. Various reconstruction algorithms have been studied, including $\ell_1$ and nuclear norm minimization as well as…
Matrices with low-rank structure are ubiquitous in scientific computing. Choosing an appropriate rank is a key step in many computational algorithms that exploit low-rank structure. However, estimating the rank has been done largely in an…
In this paper, we study the problem of image recovery from given partial (corrupted) observations. Recovering an image using a low-rank model has been an active research area in data analysis and machine learning. But often, images are not…
Low rank approximation is an important tool used in many applications of signal processing and machine learning. Recently, randomized sketching algorithms were proposed to effectively construct low rank approximations and obtain approximate…
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…
We consider the matrix completion problem of recovering a structured low rank matrix with partially observed entries with mixed data types. Vast majority of the solutions have proposed computationally feasible estimators with strong…
Low-rank representation~(LRR) has been a significant method for segmenting data that are generated from a union of subspaces. It is, however, known that solving the LRR program is challenging in terms of time complexity and memory…
The recovery of the underlying low-rank structure of clean data corrupted with sparse noise/outliers is attracting increasing interest. However, in many low-level vision problems, the exact target rank of the underlying structure and the…
This paper focuses on recovering an underlying matrix from its noisy partial entries, a problem commonly known as matrix completion. We delve into the investigation of a non-convex regularization, referred to as transformed $L_1$ (TL1),…
This paper considers the problem of finding a low rank matrix from observations of linear combinations of its elements. It is well known that if the problem fulfills a restricted isometry property (RIP), convex relaxations using the nuclear…
While leverage score sampling provides powerful tools for approximating solutions to large least squares problems, the cost of computing exact scores and sampling often prohibits practical application. This paper addresses this challenge by…
The task of estimating a matrix given a sample of observed entries is known as the \emph{matrix completion problem}. Most works on matrix completion have focused on recovering an unknown real-valued low-rank matrix from a random sample of…
We study the completion of approximately low rank matrices with entries missing not at random (MNAR). In the context of typical large-dimensional statistical settings, we establish a framework for the performance analysis of the nuclear…
This paper deals with the trace regression model where $n$ entries or linear combinations of entries of an unknown $m_1\times m_2$ matrix $A_0$ corrupted by noise are observed. We propose a new nuclear norm penalized estimator of $A_0$ and…
The paper presents several results that address a fundamental question in low-rank matrices recovery: how many measurements are needed to recover low rank matrices? We begin by investigating the complex matrices case and show that…
Numerous applications in data mining and machine learning require recovering a matrix of minimal rank. Robust principal component analysis (RPCA) is a general framework for handling this kind of problems. Nuclear norm based convex surrogate…
We consider the problem of recovering a low-rank matrix from its clipped observations. Clipping is conceivable in many scientific areas that obstructs statistical analyses. On the other hand, matrix completion (MC) methods can recover a…
We consider the problem of recovering a low-multilinear-rank tensor from a small amount of linear measurements. We show that the Riemannian gradient algorithm initialized by one step of iterative hard thresholding can reconstruct an…
This paper deals with the problem of robust matrix completion -- retrieving a low-rank matrix and a sparse matrix from the compressed counterpart of their superposition. Though seemingly not an unresolved issue, we point out that the…
We develop two iterative algorithms for solving the low rank phase retrieval (LRPR) problem. LRPR refers to recovering a low-rank matrix $\X$ from magnitude-only (phaseless) measurements of random linear projections of its columns. Both…