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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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Proceedings ArticleDOI
Sparse Signal Detection from Incoherent Projections
TL;DR: This paper demonstrates how CS principles can solve signal detection problems given incoherent measurements without ever reconstructing the signals involved, and proposes an incoherent detection and estimation algorithm (IDEA) based on matching pursuit.
Book ChapterDOI
Robust and fast collaborative tracking with two stage sparse optimization
TL;DR: This work proposes a novel online tracking algorithm with two stage sparse optimization to jointly minimize the target reconstruction error and maximize the discriminative power and dynamic group sparsity (DGS) is utilized in this algorithm.
Journal ArticleDOI
Intelligent Secured Two-Way Image Transmission Using Corvus Corone Module over WSN
TL;DR: This paper proposed two-way image transmission to the Corvus Coron module, which presents an energy-effective with the CS model, as an inbuilt interaction in the CS transmission through the security framework, which results in energy-efficient and conserved transmission in the form of low error rate with low computational time.
Journal ArticleDOI
Dictionary Learning and Time Sparsity for Dynamic MR Data Reconstruction
TL;DR: An iterative algorithm is presented that enables the application of DL for the reconstruction of cardiac cine data with Cartesian undersampling and is compared to and shown to systematically outperform k- t FOCUSS, a successful CS method that uses a fixed basis transform.
Journal ArticleDOI
The Orthogonal Super Greedy Algorithm and Applications in Compressed Sensing
Entao Liu,Vladimir Temlyakov +1 more
TL;DR: A new greedy algorithm which is called the orthogonal super greedy algorithm (OSGA), called OSGA, is built and it is observed that OSGA is times simpler (more efficient) than OMP.
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.