J. Tropp

Publications157
h-index53
Citations34,585
Highly Influential Citations3,910
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Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
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 ln…
View on IEEE
Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions
TLDR
This work surveys and extends recent research which demonstrates that randomization offers a powerful tool for performing low-rank matrix approximation, and presents a modular framework for constructing randomized algorithms that compute partial matrix decompositions.
View PDF on arXiv
CoSaMP: Iterative signal recovery from incomplete and inaccurate samples
TLDR
This extended abstract describes a recent algorithm, called, CoSaMP, that accomplishes the data recovery task and was the first known method to offer near-optimal guarantees on resource usage.
View PDF on arXiv
Greed is good: algorithmic results for sparse approximation
  • J. Tropp
  • Computer Science
    IEEE Transactions on Information Theory
  • 1 October 2004
TLDR
This article presents new results on using a greedy algorithm, orthogonal matching pursuit (OMP), to solve the sparse approximation problem over redundant dictionaries and develops a sufficient condition under which OMP can identify atoms from an optimal approximation of a nonsparse signal.
View on IEEE
User-Friendly Tail Bounds for Sums of Random Matrices
  • J. Tropp
  • Mathematics
    Found. Comput. Math.
  • 25 April 2010
TLDR
This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices and provides noncommutative generalizations of the classical bounds associated with the names Azuma, Bennett, Bernstein, Chernoff, Hoeffding, and McDiarmid.
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Algorithms for simultaneous sparse approximation. Part I: Greedy pursuit
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An Introduction to Matrix Concentration Inequalities
  • J. Tropp
  • Mathematics
    Found. Trends Mach. Learn.
  • 7 January 2015
TLDR
The aim of this monograph is to describe the most successful methods from this area along with some interesting examples that these techniques can illuminate.
View PDF on arXiv
Just relax: convex programming methods for identifying sparse signals in noise
  • J. Tropp
  • Computer Science
    IEEE Transactions on Information Theory
  • 1 March 2006
TLDR
A method called convex relaxation, which attempts to recover the ideal sparse signal by solving a convex program, which can be completed in polynomial time with standard scientific software.
View on IEEE
Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals
TLDR
A new type of data acquisition system, called a random demodulator, that is constructed from robust, readily available components that supports the empirical observations, and a detailed theoretical analysis of the system's performance is provided.
View on IEEE
SIGNAL RECOVERY FROM PARTIAL INFORMATION VIA ORTHOGONAL MATCHING PURSUIT
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(m…
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