Open Access
Signal Recovery from Random Measurements Via Orthogonal Matching Pursuit: The Gaussian Case
Joel A. Tropp,Anna C. Gilbert +1 more
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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
Recovery of sparse signals using OMP and its variants: convergence analysis based on RIP
Shisheng Huang,Jubo Zhu +1 more
TL;DR: The convergence property of OMP based on the restricted isometry property (RIP) is analyzed, and it is shown that the OMP algorithm can exactly recover an arbitrary K-sparse signal using K steps provided that the sampling matrix Φ satisfies the RIP with parameter .
Journal ArticleDOI
Transient Feature Extraction by the Improved Orthogonal Matching Pursuit and K-SVD Algorithm With Adaptive Transient Dictionary
TL;DR: The simulated and experimental results show that the proposed method can not only much faster extract the fault characteristics than the traditional K-SVD method, but also more accurately detect the repetitive transients than the infogram method and the traditional SVD method.
Book ChapterDOI
A compressed sensing approach for MR tissue contrast synthesis
TL;DR: Experiments on real data, obtained using different scanners and pulse sequences, show improvement in segmentation consistency, which could be extremely valuable in the pooling of multi-site multi-scanner neuroimaging studies.
Journal ArticleDOI
Support Recovery With Orthogonal Matching Pursuit in the Presence of Noise
TL;DR: This article studies the orthogonal matching pursuit (OMP) algorithm for the recovery of support under noise and shows that recovery with an arbitrarily small but constant fraction of errors is possible with the OMP algorithm.
Journal ArticleDOI
Efficient fusion for infrared and visible images based on compressive sensing principle
Xiaoqiang Li,S.-Y. Qin +1 more
TL;DR: A novel self-adaptive weighted average fusion scheme based on standard deviation of measurements to merge IR and visible images is developed in the special domain of CS using the better recovery tool of total variation optimisation and achieves a high level of fusion quality in human perception of global information.
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.