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
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Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control
Steven L. Brunton,J. Nathan Kutz +1 more
TL;DR: In this paper, the authors bring together machine learning, engineering mathematics, and mathematical physics to integrate modeling and control of dynamical systems with modern methods in data science, and highlight many of the recent advances in scientific computing that enable data-driven methods to be applied to a diverse range of complex systems, such as turbulence, the brain, climate, epidemiology, finance, robotics, and autonomy.
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Analysis of Orthogonal Matching Pursuit Using the Restricted Isometry Property
TL;DR: This paper demonstrates that the restricted isometry property (RIP) can be used for a very straightforward analysis of OMP and concludes that the RIP of order K+1 (with isometry constant δ <; [ 1/( 3√K)]) is sufficient for OMP to exactly recover any K-sparse signal.
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Beamforming for Millimeter Wave Communications: An Inclusive Survey
Shajahan Kutty,Debarati Sen +1 more
TL;DR: The suitability of millimeter wave beamforming methods, both, existing and proposed till midyear 2015, are explored, and the exciting new prospects unfolding in this domain are identified.
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Application of compressive sensing to sparse channel estimation
TL;DR: It is pointed out that a popular assumption - that multipath channels are sparse in their equivalent baseband representation - has pitfalls and there are over-complete dictionaries that lead to much sparser channel representations and better estimation performance.
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Image melding: combining inconsistent images using patch-based synthesis
TL;DR: This work presents a new method for synthesizing a transition region between two source images, such that inconsistent color, texture, and structural properties all change gradually from one source to the other, calling this process image melding.
References
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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.
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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.
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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.