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- Joel A. Tropp, Anna C. Gilbert
- IEEE Transactions on Information Theory
- 2007

This paper demonstrates theoretically and empirically that a greedy algorithm called orthogonal matching pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension d given O(m lnâ€¦ (More)

- Nathan Halko, Per-Gunnar Martinsson, Joel A. Tropp
- SIAM Review
- 2011

Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This workâ€¦ (More)

- Joel A. Tropp, Deanna Needell
- Commun. ACM
- 2010

Compressive sampling (CoSa) is a new paradigm for developing data sampling technologies. It is based on the principle that many types of vector-space data are compressible, which is a term of art inâ€¦ (More)

- Joel A. Tropp
- IEEE Transactions on Information Theory
- 2004

This article presents new results on using a greedy algorithm, orthogonal matching pursuit (OMP), to solve the sparse approximation problem over redundant dictionaries. It provides a sufficientâ€¦ (More)

- Joel A. Tropp, Anna C. Gilbert, Martin Strauss
- Signal Processing
- 2006

A simultaneous sparse approximation problem requests a good approximation of several input signals at once using different linear combinations of the same elementary signals. At the same time, theâ€¦ (More)

- Joel A. Tropp
- Foundations of Computational Mathematics
- 2012

This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices. These results place simple and easily verifiable hypotheses on the summands, and they deliverâ€¦ (More)

- Joel A. Tropp
- IEEE Transactions on Information Theory
- 2006

This paper studies a difficult and fundamental problem that arises throughout electrical engineering, applied mathematics, and statistics. Suppose that one forms a short linear combination ofâ€¦ (More)

This article demonstrates theoretically and empirically that a greedy algorithm called Orthogonal Matching Pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension d given O(mâ€¦ (More)

- Joel A. Tropp, Anna C. Gilbert, Martin Strauss
- Proceedings. (ICASSP '05). IEEE Internationalâ€¦
- 2005

A simple sparse approximation problem requests an approximation of a given input signal as a linear combination of T elementary signals drawn from a large, linearly dependent collection. An importantâ€¦ (More)