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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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Dictionary Training for Sparse Representation as Generalization of K-Means Clustering
Sujit Kumar Sahoo,Anamitra Makur +1 more
TL;DR: This letter investigates dictionary training algorithms for sparse representation like K-SVD, MOD, and their variation from that viewpoint and proposes an alternative to MOD; a sequential generalization of K-means (SGK), which shows MOD and SGK to be faster under a dimensionality condition.
Proceedings ArticleDOI
Direct inference on compressive measurements using convolutional neural networks
TL;DR: This paper shows that convolutional neural networks (CNNs) can be employed to extract discriminative non-linear features directly from CS measurements, and demonstrates that effective high-level inference can be performed.
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Direct simulation of random field samples from sparsely measured geotechnical data with consideration of uncertainty in interpretation
TL;DR: A novel random field generator is developed, which is capable of directly generating RFSs from sparse measurements obtained during site characterization and properly accounting for uncertainty associated with interpretation of sparse data.
Journal ArticleDOI
Tongue tumor detection in medical hyperspectral images.
Zhi Liu,Hongjun Wang,Qingli Li +2 more
TL;DR: The experimental results show that hyperspectral imaging for tongue tumor diagnosis, together with the spectroscopic classification method provide a new approach for the noninvasive computer-aided diagnosis of tongue tumors.
Journal ArticleDOI
Model recovery for Hammerstein systems using the auxiliary model based orthogonal matching pursuit method
TL;DR: The auxiliary model based orthogonal matching pursuit algorithm can simultaneously identify parameters and orders of the Hammerstein system, and has a high efficient identification performance.
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.