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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 Sparsification Approach to Set Membership Identification of Switched Affine Systems
TL;DR: The key idea of the paper is to reduce the problem of robust identification of a class of discrete-time affine hybrid systems, switched affine models, in a set membership framework to a sparsification form, where the goal is to maximize sparsity of a suitably constructed vector sequence.
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Time-Frequency Training OFDM with High Spectral Efficiency and Reliable Performance in High Speed Environments
TL;DR: A fundamentally distinct OFDM-based transmission scheme called time-frequency training OFDM (TFT-OFDM) is proposed, whereby every TFT- OFDM symbol has training information both in the time and frequency domains.
Journal ArticleDOI
Compressive Sensing of a Taylor-Fourier Multifrequency Model for Synchrophasor Estimation
TL;DR: A new compressive sensing (CS) approach is introduced and applied to synchrophasor measurements using a CS Taylor-Fourier (TF) multifrequency (CSTFM) model to exploit the properties of CS and the TF transform to identify the most relevant components of the signal, even under dynamic conditions, and model them in the estimation procedure, thus limiting the impact of harmonic and interhamonic interferences.
Journal ArticleDOI
Finding Deterministic Solution From Underdetermined Equation: Large-Scale Performance Variability Modeling of Analog/RF Circuits
TL;DR: A novel L0-norm regularization method is adapted to address the modeling challenge of aggressive scaling of integrated circuit technology and achieves up to 25× speedup compared to the traditional least-squares fitting method.
Journal ArticleDOI
A survey on compressive sensing techniques for cognitive radio networks
TL;DR: This paper provides an in depth survey on compressive sensing techniques and classifies these techniques according to which process they target, namely, sparse representation, sensing matrix, or recovery algorithms.
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.