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
Secure and Robust Iris Recognition Using Random Projections and Sparse Representations
TL;DR: This paper proposes a unified framework based on random projections and sparse representations that can simultaneously address all three issues mentioned above in relation to iris biometrics, and includes enhancements to privacy and security by providing ways to create cancelable iris templates.
Journal ArticleDOI
Compressive Sensing in Electromagnetics - A Review
TL;DR: A review of the state-of-the-art and most recent advances of compressive sensing and related methods as applied to electromagnetics can be found in this article, where a wide set of applicative scenarios comprising the diagnosis and synthesis of antenna arrays, the estimation of directions of arrival, and the solution of inverse scattering and radar imaging problems are reviewed.
Proceedings ArticleDOI
Real-time visual tracking using compressive sensing
TL;DR: Real-time Com-pressive Sensing Tracking (RTCST) as mentioned in this paper exploits the signal recovery power of compressive sensing (CS), and adopts Dimensionality Reduction and a customized Orthogonal Matching Pursuit (OMP) algorithm to accelerate the CS tracking.
Journal ArticleDOI
Optimally Tuned Iterative Reconstruction Algorithms for Compressed Sensing
Arian Maleki,David L. Donoho +1 more
TL;DR: It is shown that the phase transition is a well-defined quantity with the suite of random underdetermined linear systems chosen, and the optimally tuned algorithms dominate such proposals.
Journal ArticleDOI
Ultra-Wideband Compressed Sensing: Channel Estimation
TL;DR: Extensive simulations show that for different propagation scenarios and UWB communication channels, detectors based on CS channel estimation outperform traditional correlator using just 1/3 of the sampling rate leading thus to a reduced use of analog-to-digital resources in the channel estimation stage.
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.