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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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Robust flow field reconstruction from limited measurements via sparse representation
TL;DR: In this paper, the authors explore sparse representation for flow reconstruction on a variety of fluid data sets with a wide range of complexity, including vortex shedding past a cylinder at low Reynolds number, a mixing layer, and two geophysical flows.
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Compressive Rendering: A Rendering Application of Compressed Sensing
Pradeep Sen,Soheil Darabi +1 more
TL;DR: A novel application of compressed sensing is proposed by using it to accelerate ray-traced rendering in a manner that exploits the sparsity of the final image in the wavelet basis, and can achieve high-quality images with approximately 75 percent of the pixel samples using a nonadaptive sampling scheme.
Journal ArticleDOI
Interpretation of soil property profile from limited measurement data: a compressive sampling perspective
Yu Wang,Tengyuan Zhao +1 more
TL;DR: This paper aims to address the problem and develop an approach to determine the soil property profile from a limited number of measurement points when only limited measurement data are available.
Journal ArticleDOI
Unsupervised Blind Image Quality Evaluation via Statistical Measurements of Structure, Naturalness, and Perception
TL;DR: This paper initiatively introduces the perception quality measurement into the construction of unsupervised BIQA method, which is conducted by characterizing the prediction discrepancy between the image and its brain prediction based on the free-energy principle in the newly revealed brain theory.
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Sample diversity, representation effectiveness and robust dictionary learning for face recognition
TL;DR: Experimental results demonstrate that the proposed algorithm framework outperforms some previous state-of-the-art dictionary learning and sparse coding algorithms in face recognition and can be applied to other pattern classification tasks.
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.
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.