Open Access
Signal Recovery from Random Measurements Via Orthogonal Matching Pursuit: The Gaussian Case
Joel A. Tropp,Anna C. Gilbert +1 more
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
Compressed Meter Reading for Delay-Sensitive and Secure Load Report in Smart Grid
TL;DR: The random sequence used in the compressed sensing enhances the privacy and integrity of the meter reading and results in uniform delays, in contrast to the possible large delay in carrier sensing multiple access (CSMA) technique.
Journal ArticleDOI
Statistical interpretation of soil property profiles from sparse data using Bayesian compressive sampling
Yu Wang,Tengyuan Zhao +1 more
TL;DR: In this article, a Bayesian compressive sampling (BCS) method is proposed to address the problem of uncertainty in the interpretation of a soil property profile from sparse measurement data.
Journal ArticleDOI
A Fully Integrated Wireless Compressed Sensing Neural Signal Acquisition System for Chronic Recording and Brain Machine Interface
Xilin Liu,Milin Zhang,Tao Xiong,Andrew G. Richardson,Timothy H. Lucas,Peter S. Chin,Ralph Etienne-Cummings,Trac D. Tran,Jan Van der Spiegel +8 more
TL;DR: An optimized wireless compressed sensing neural signal recording system that achieves high signal recording quality with minimized power consumption, while reducing the risk of infection from through-skin connectors has been successfully used for long-term wireless neural recording in freely behaving rhesus monkey.
Journal ArticleDOI
A Survey of Dictionary Learning Algorithms for Face Recognition
TL;DR: A survey of dictionary learning algorithms for face recognition is provided to understand the profiles of this subject and to grasp the theoretical rationales and potentials as well as their applicability to different cases of face recognition.
Journal ArticleDOI
Hyperspectral Image Classification Via Shape-Adaptive Joint Sparse Representation
TL;DR: A new shape-adaptive joint sparse representation classification (SAJSRC) method is proposed for hyperspectral images (HSIs) classification that adaptively explores the spatial information and incorporates it into a joint sparse representations classifier.
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.