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
Efficient Bayesian inference of subsurface flow models using nested sampling and sparse polynomial chaos surrogates
TL;DR: A two-stage sampling using a polynomial chaos response surface to filter out rejected samples in the Markov Chain Monte-Carlo method is performed.
Proceedings ArticleDOI
High-speed compressed sensing reconstruction on FPGA using OMP and AMP
TL;DR: In this paper, the authors present generic high-speed FPGA implementations of orthogonal matching pursuit (OMP) and approximate message passing (AMP) algorithms for image reconstruction.
Journal ArticleDOI
Subspace Matching Pursuit for Sparse Unmixing of Hyperspectral Data
TL;DR: Inspired by the existing SGA methods, a novel GA termed subspace matching pursuit (SMP) is presented, which makes use of the low-degree mixed pixels in the hyperspectral image to iteratively find a subspace to reconstruct the Hyperspectral data and can serve as a dictionary pruning algorithm.
Journal ArticleDOI
Compressed Sensing of Complex Sinusoids: An Approach Based on Dictionary Refinement
TL;DR: This work model the sparsifying Fourier dictionary as a parameterized dictionary, with the sampled frequency grid points treated as the underlying parameters, and develops a novel recovery algorithm for CS of complex sinusoids based on the philosophy of the variational expectation-maximization (EM) algorithm.
Journal ArticleDOI
NuMax: A Convex Approach for Learning Near-Isometric Linear Embeddings
TL;DR: A novel framework for the deterministic construction of linear, near-isometric embeddings of a finite set of data points and develops a greedy, approximate version of NuMax based on the column generation method commonly used to solve large-scale linear programs.
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.