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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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Journal ArticleDOI
Interpolation of spatially varying but sparsely measured geo-data: A comparative study
TL;DR: In this paper, Bayesian compressive sampling (BCS) has been used to estimate the geology properties of interest at unobserved locations in engineering geology practice, particularly for projects with medium or relatively small sizes.
Journal ArticleDOI
A Unified Design of Massive Access for Cellular Internet of Things
TL;DR: A three-phase transmission protocol which consists of device detection and channel estimation, uplink data transmission, and downlink data transmission for the cellular IoT, so as to realize massive access over limited radio spectrum is designed.
Journal ArticleDOI
An adaptive fusion approach for infrared and visible images based on NSCT and compressed sensing
Qiong Zhang,Xavier Maldague +1 more
TL;DR: A novel nonsubsampled contourlet transform transform (NSCT) based image fusion approach, implementing an adaptive-Gaussian fuzzy membership method, compressed sensing technique, total variation based gradient descent reconstruction algorithm, is proposed for the fusion computation of infrared and visible images.
Journal ArticleDOI
Lorentzian Iterative Hard Thresholding: Robust Compressed Sensing With Prior Information
TL;DR: Simulation results demonstrate that the Lorentzian-based IHT algorithm significantly outperform commonly employed sparse reconstruction techniques in impulsive environments, while providing comparable performance in less demanding, light-tailed environments.
DissertationDOI
Compressive sensing: a summary of reconstruction algorithms
TL;DR: A new algorithm (the Modified Frame Reconstruction or MFR algorithm) for signal reconstruction in compressive sensing generalises previous iterative hard thresholding algorithms and dramatically increases both the success rate and the rate of convergence of the modified algorithms in comparison to the un-modified algorithm.
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.