Open Access
Signal Recovery from Random Measurements Via Orthogonal Matching Pursuit: The Gaussian Case
Joel A. Tropp,Anna C. Gilbert +1 more
TLDR
In this paper, a greedy algorithm called Orthogonal Matching Pursuit (OMP) was proposed to recover a signal with m nonzero entries in dimension 1 given O(m n d) random linear measurements of that signal.Abstract:
This report 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(mln d) random linear measurements of that signal. This is a massive improvement
over previous results, which require O(m2) measurements. The new results for OMP are comparable
with recent results for another approach called Basis Pursuit (BP). In some settings, the
OMP algorithm is faster and easier to implement, so it is an attractive alternative to BP for signal
recovery problems.read more
Citations
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Journal ArticleDOI
Gradient Pursuits
Thomas Blumensath,Michael Davies +1 more
TL;DR: Improvements to greedy strategies are proposed and algorithms are developed that approximate orthogonal matching pursuit with computational requirements more akin to matching pursuit, with the approximate conjugate gradient method being superior to the gradient method.
Journal ArticleDOI
Compressive Sensing by Random Convolution
TL;DR: It is shown that an n-dimensional signal which is S-sparse in any fixed orthonormal representation can be recovered from m samples from its convolution with a pulse whose Fourier transform has unit magnitude and random phase at all frequencies.
Journal ArticleDOI
Compressed Sensing and Redundant Dictionaries
TL;DR: It is shown that a matrix, which is a composition of a random matrix of certain type and a deterministic dictionary, has small restricted isometry constants, and signals that are sparse with respect to the dictionary can be recovered via basis pursuit from a small number of random measurements.
Journal ArticleDOI
Advances on Spectrum Sensing for Cognitive Radio Networks: Theory and Applications
Abdelmohsen Ali,Walaa Hamouda +1 more
TL;DR: This survey paper focuses on the enabling techniques for interweave CR networks which have received great attention from standards perspective due to its reliability to achieve the required quality-of-service.
Journal ArticleDOI
Solving inverse problems using data-driven models
TL;DR: This survey paper aims to give an account of some of the main contributions in data-driven inverse problems.
References
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Book
Compressed sensing
TL;DR: It is possible to design n=O(Nlog(m)) nonadaptive measurements allowing reconstruction with accuracy comparable to that attainable with direct knowledge of the N most important coefficients, and a good approximation to those N important coefficients is extracted from the n measurements by solving a linear program-Basis Pursuit in signal processing.
Journal ArticleDOI
Atomic Decomposition by Basis Pursuit
TL;DR: Basis Pursuit (BP) is a principle for decomposing a signal into an "optimal" superposition of dictionary elements, where optimal means having the smallest l1 norm of coefficients among all such decompositions.
Journal ArticleDOI
Matching pursuits with time-frequency dictionaries
Stéphane Mallat,Zhifeng Zhang +1 more
TL;DR: The authors introduce an algorithm, called matching pursuit, that decomposes any signal into a linear expansion of waveforms that are selected from a redundant dictionary of functions, chosen in order to best match the signal structures.
Journal ArticleDOI
Least angle regression
Bradley Efron,Trevor Hastie,Iain M. Johnstone,Robert Tibshirani,Hemant Ishwaran,Keith Knight,Jean-Michel Loubes,Jean-Michel Loubes,Pascal Massart,Pascal Massart,David Madigan,David Madigan,Greg Ridgeway,Greg Ridgeway,Saharon Rosset,Saharon Rosset,Ji Zhu,Robert A. Stine,Berwin A. Turlach,Sanford Weisberg +19 more
TL;DR: A publicly available algorithm that requires only the same order of magnitude of computational effort as ordinary least squares applied to the full set of covariates is described.