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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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Benchmarking a Multimodal and Multiview and Interactive Dataset for Human Action Recognition
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Low-dimensional signal-strength fingerprint-based positioning in wireless LANs
Dimitris Milioris,George Tzagkarakis,Artemis Papakonstantinou,Maria Papadopouli,Panagiotis Tsakalides +4 more
TL;DR: A suite of novel indoor positioning techniques utilizing signal-strength fingerprints collected from access points and compressive sensing to perform sparsity-based accurate indoor localization, while reducing significantly the amount of information transmitted from a wireless device, possessing limited power, storage, and processing capabilities, to a central server is introduced.
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Fast Sparse Superposition Codes Have Near Exponential Error Probability for $R
Antony Joseph,Andrew R. Barron +1 more
TL;DR: Here, a fast decoding algorithm, called the adaptive successive decoder, is developed, and for any rate R less than the capacity C, communication is shown to be reliable with nearly exponentially small error probability.
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Cloud K-SVD: A Collaborative Dictionary Learning Algorithm for Big, Distributed Data
Haroon Raja,Waheed U. Bajwa +1 more
TL;DR: An analysis of cloud K-SVD is provided that gives insights into its properties as well as deviations of the dictionaries learned at individual sites from a centralized solution in terms of different measures of local/global data and topology of interconnections.
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Exploiting Prior Knowledge in Compressed Sensing Wireless ECG Systems
TL;DR: In this article, the authors exploit the structure of the wavelet representation of the ECG signal to boost the performance of compressed sensing-based methods for compression and reconstruction of ECG signals.
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.