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The Annals of Statistics, ISSN 0090-5364, 8/2012, Volume 40, Issue 4, pp. 2195 - 2238
Journal Article
Foundations of Computational Mathematics, ISSN 1615-3375, 12/2009, Volume 9, Issue 6, pp. 717 - 772
We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries... 
Nuclear norm minimization | Random matrices | Decoupling | Noncommutative Khintchine inequality | Convex optimization | Duality in optimization | Compressed sensing | Low-rank matrices | Matrix completion | MATHEMATICS, APPLIED | INEQUALITIES | U-STATISTICS | MATHEMATICS | COMPUTER SCIENCE, THEORY & METHODS
Journal Article
The Annals of Statistics, ISSN 0090-5364, 10/2015, Volume 43, Issue 5, pp. 2055 - 2085
Journal Article
Foundations of Computational Mathematics, ISSN 1615-3375, 06/2015, Volume 15, Issue 3, pp. 715 - 732
In this paper we introduce a simple heuristic adaptive restart technique that can dramatically improve the convergence rate of accelerated gradient schemes.... 
Convex optimization | First order methods | Accelerated gradient schemes | MATHEMATICS | MATHEMATICS, APPLIED | LINEAR INVERSE PROBLEMS | SHRINKAGE | THRESHOLDING ALGORITHM | COMPUTER SCIENCE, THEORY & METHODS | Analysis | Convergence (Mathematics) | Iterative methods (Mathematics) | Optimization algorithms | Heuristics | Computational mathematics
Journal Article
Communications on Pure and Applied Mathematics, ISSN 0010-3640, 06/2014, Volume 67, Issue 6, pp. 906 - 956
This paper develops a mathematical theory of super‐resolution. Broadly speaking, super‐resolution is the problem of recovering the fine details of an... 
SUPERRESOLUTION | SPARSITY | MATHEMATICS | MATHEMATICS, APPLIED | UNCERTAINTY PRINCIPLES | RECONSTRUCTION | ALGORITHM | SIGNALS | INNOVATION | FINITE RATE | Mathematical problems | Theory | Optimization
Journal Article
Communications on Pure and Applied Mathematics, ISSN 0010-3640, 08/2013, Volume 66, Issue 8, pp. 1241 - 1274
Suppose we wish to recover a signal \input amssym $\font\abc=cmmib10\def\bi#1{\hbox{\abc#1}} {\bi x} \in {\Bbb C}^n$ from m intensity measurements of the form... 
MATHEMATICS | MATHEMATICS, APPLIED | RETRIEVAL | Mathematical problems | Measurement | Probability distribution | Mathematical programming
Journal Article
Inverse Problems, ISSN 0266-5611, 06/2007, Volume 23, Issue 3, pp. 969 - 985
We consider the problem of reconstructing a sparse signal x(0) is an element of R-n from a limited number of linear measurements. Given m randomly selected... 
MATHEMATICS, APPLIED | EMPIRICAL PROCESSES | BASES | REPRESENTATIONS | SIGNAL RECOVERY | CONCENTRATION INEQUALITIES | MAXIMA | PHYSICS, MATHEMATICAL | ROBUST UNCERTAINTY PRINCIPLES
Journal Article
Comptes rendus - Mathématique, ISSN 1631-073X, 2008, Volume 346, Issue 9, pp. 589 - 592
It is now well-known that one can reconstruct sparse or compressible signals accurately from a very limited number of measurements, possibly contaminated with... 
MATHEMATICS
Journal Article
IEEE Transactions on Information Theory, ISSN 0018-9448, 04/2011, Volume 57, Issue 4, pp. 2342 - 2359
Journal Article