We show that by randomizing the column signs of such a matrix Phi, the resulting map with high probability embeds any fixed set of p = O(e^k) points in R^N into R^m without distorting the norm of any point in the set by more than a factor of 1 +- delta.Expand

In many signal processing applications, one wishes to acquire images that are sparse in transform domains such as spatial finite differences or wavelets using frequency domain samples.Expand

We show that a Legendre s-sparse polynomial of maximal degree N can be recovered from [emailÂ protected]?slog^4(N) random samples that are chosen independently according to the Chebyshev probability measure. As an efficient recovery method, @?"1-minimization can be used.Expand

This paper presents near-optimal guarantees for stable and robust image recovery from undersampled noisy measurements using total variation minimization.Expand

Matrix completion, i.e., the exact and provable recovery of a low rank matrix from a small subset of its elements, is currently only known to be possible if the matrix satisfies a restrictive structural constraint---known as {\em incoherence}---on its row and column spaces.Expand

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 with an error of the order of the best $k$-rank approximation.Expand

We study exact recovery conditions for convex relaxations of point cloud clustering problems, focusing on two of the most common optimization problems for unsupervised clustering: k-means and k-median clustering.Expand

Functions of interest are often smooth and sparse in some sense, and both priors should be taken into account when interpolating sampled data. Classical linear interpolation methods are effectiveâ€¦ Expand