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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Journal ArticleDOI
Compressive Sensing With Prior Support Quality Information and Application to Massive MIMO Channel Estimation With Temporal Correlation
Xiongbin Rao,Vincent K. N. Lau +1 more
TL;DR: The distortion bound of the recovered signal from the proposed algorithm is analyzed and it is shown that a better quality prior support can lead to better CS recovery performance.
Journal ArticleDOI
DOA Estimation Exploiting Moving Dilated Nested Arrays
TL;DR: A novel dilated nested array is presented to obtain an enhanced fully filled difference coarray exploiting array motions to provide direction-of-arrival (DOA) estimation and to validate array analyses.
Journal ArticleDOI
Sensor Technologies for Fall Detection Systems: A Review
TL;DR: This review provides a comprehensive overview of each competing sensor technology ranging from an accelerometer, pressure sensor, and radar to camera-based and their infusion into a complete fall detection system.
Patent
Separation and noise removal for multiple vibratory source seismic data
TL;DR: In this paper, a method to recover separated seismograms with reduced interference noise by processing vibroseis data recorded (or computer simulated) with multiple vibrators shaking simultaneously or nearly simultaneously was proposed.
Journal ArticleDOI
Simultaneous discriminative projection and dictionary learning for sparse representation based classification
TL;DR: This paper proposes to learn simultaneously a discriminative projection and a dictionary that are optimized for the sparse representation based classifier, to extract discriminatives information from the raw data while respecting the sparse Representation assumption.
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.