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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Book ChapterDOI
Sparse methods for direction-of-arrival estimation
TL;DR: An overview of these sparse methods for DOA estimation is provided, with a particular highlight on the recently developed gridless sparse methods, e.g., those based on covariance fitting and the atomic norm.
Journal ArticleDOI
A New Family of Model-Based Impulsive Wavelets and Their Sparse Representation for Rolling Bearing Fault Diagnosis
TL;DR: This paper explores a new impulsive feature extraction method based on the sparse representation that demonstrates its advantage and superiority in weak repetitive transient feature extraction.
Proceedings ArticleDOI
Compressed Sensing Framework for EEG Compression
TL;DR: A compressed sensing framework is introduced for efficient representation of multichannel, multiple trial EEG data and a simultaneous orthogonal matching pursuit algorithm is shown to be effective in the joint recovery of the original multiple trail EEG signals from a small number of projections.
Journal ArticleDOI
Compressive Two-Dimensional Harmonic Retrieval via Atomic Norm Minimization
Yuejie Chi,Yuxin Chen +1 more
TL;DR: It is demonstrated that under some mild spectral separation condition, it is possible to exactly recover all frequencies by solving an atomic norm minimization program, as long as the sample complexity exceeds the order of rlogrlogn.
Journal ArticleDOI
Random Sampling of Sparse Trigonometric Polynomials, II. Orthogonal Matching Pursuit versus Basis Pursuit
Stefan Kunis,Holger Rauhut +1 more
TL;DR: In this article, the authors investigate the problem of reconstructing sparse multivariate trigonometric polynomials from few randomly taken samples by Basis Pursuit and greedy algorithms such as Orthogonal Matching Pursuit (OMP) and Thresholding.
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.