Open Access
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 Fast TVL1-L2 Minimization Algorithm for Signal Reconstruction from Partial Fourier Data
Junfeng Yang,Yin Zhang,Wotao Yin +2 more
TL;DR: This paper proposes a simple and fast algorithm for signal reconstruction from partial Fourier data that minimizes the sum of three terms corresponding to total variation, `1-norm regularization and least squares data fitting, and uses an alternating minimization scheme.
Journal ArticleDOI
A Novel STAP Based on Spectrum-Aided Reduced-Dimension Clutter Sparse Recovery
TL;DR: By solving a reduced-dimension sparse recovery problem, the computational load of the proposed method can be reduced significantly while only slightly degrading the performance of clutter suppression and target detection compared with current SR-STAP methods.
Journal ArticleDOI
Parameterizing both path amplitude and delay variations of underwater acoustic channels for block decoding of orthogonal frequency division multiplexing
TL;DR: For channels with a short coherence time, the numerical results show that incorporating both the amplitude and delay variations improves the system performance, and one polynomial up to the first order is proposed to approximate the amplitude variation.
Posted Content
Phase Transitions for Greedy Sparse Approximation Algorithms
TL;DR: In this article, the authors present a framework in which translates RIP-based sufficient conditions for Gaussian measurement matrices into requirements on the signal's sparsity level, length, and number of measurements.
Journal ArticleDOI
Cluster-Tree Routing Based Entropy Scheme for Data Gathering in Wireless Sensor Networks
TL;DR: Simulation results reveal that the proposed scheme outperforms existing baseline algorithms in terms of stability period, network lifetime, and average normalized mean squared error for compressive sensing data reconstruction.
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.
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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.
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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.
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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.