• Publications
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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
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.
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.
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.
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.
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.
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.
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.
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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