The goal of the sparse approximation problem is to approximate a target signal using a
linear combination of a few elementary signals drawn from a fixed collection. This paper …

In this paper we study the problem of recovering a low-rank matrix from linear
measurements. Our algorithm, which we call Procrustes Flow, starts from an initial estimate …

Let M be an n¿× n matrix of rank r, and assume that a uniformly random subset E of its
entries is observed. We describe an efficient algorithm, which we call OptSpace, that …

The matrix completion problem is to recover a low-rank matrix from a subset of its entries.
The main solution strategy for this problem has been based on nuclear-norm minimization …

The problem of minimizing the rank of a matrix subject to affine constraints has applications
in several areas including machine learning, and is known to be NP-hard. A tractable …

Noisy matrix completion aims at estimating a low-rank matrix given only partial and
corrupted entries. Despite remarkable progress in designing efficient estimation algorithms …

Recovery of low-rank matrices has recently seen significant activity in many areas of science
and engineering, motivated by recent theoretical results for exact reconstruction guarantees …

There has been significant recent interest in fast imaging with sparse sampling.
Conventional imaging methods are based on Shannon-Nyquist sampling theory. As such …

In practical instances of nonconvex matrix factorization, the rank of the true solution $
r^{\star} $ is often unknown, so the rank $ r $ of the model can be over-specified as $ r> …

Subgradient methods converge linearly on a convex function that grows sharply away from
its solution set. In this work, we show that the same is true for sharp functions that are only …