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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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A real-time device-free localization system using correlated RSS measurements
TL;DR: By making full use of the consecutiveness of motion, an efficient measurement strategy based on a small set of correlated wireless links is presented and a lightweight compressed maximum matching select (CMMS) algorithm is proposed to localize target, which only needs a small-scale matrix-vector product operating for one estimation.
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Compressive Sparsity Order Estimation for Wideband Cognitive Radio Receiver
TL;DR: It is shown that the sparsity order of the wideband spectrum can be reliably estimated using the proposed technique using asymptotic eigenvalue probability distribution function of the measured signal's covariance matrix for sparse signals.
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Generalized Coprime Sampling of Toeplitz Matrices for Spectrum Estimation
TL;DR: This paper proposes a general coprime sampling scheme that implements effective compression of Toeplitz covariance matrices, and examines different schemes on covariance matrix acquisition for performance evaluation, comparison, and optimal design, based on segmented data sequences.
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Full Wavefield Analysis and Damage Imaging Through Compressive Sensing in Lamb Wave Inspections
TL;DR: The results show that the technique can be applied in a variety of structural components to reduce acquisition time and achieve high performance in defect detection and localization by removing up to 80% of the Nyquist sampling grid.
Journal ArticleDOI
Matching Pursuit LASSO Part I: Sparse Recovery Over Big Dictionary
TL;DR: A Matching Pursuit LASSO (MPL) algorithm is proposed, based on a novel quadratically constrained linear program (QCLP) formulation, which has several advantages over existing methods, and is guaranteed to converge to a global solution.
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.