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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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Journal ArticleDOI
Sparse Signal Reconstruction via Iterative Support Detection
Yilun Wang,Wotao Yin +1 more
TL;DR: An efficient implementation of ISD is introduced, called threshold-ISD, for recovering signals with fast decaying distributions of nonzeros from compressive sensing measurements, as well as two state-of-the-art algorithms: the iterative reweighted $\ell_1$ minimization algorithm (IRL1) and the iteratives reweighting least-squares algorithm ( IRLS).
Journal ArticleDOI
Manufacturing intelligent Corvus corone module for a secured two way image transmission under WSN
TL;DR: The Corvus corone module two-way image transmission is proposed that provides energy efficiency along CS model, secured transmission through a matrix of security under CS such as inbuilt method, which was named as compressed secured matrix and faultless reconstruction along that of eminent random matrix counting under CS.
Proceedings ArticleDOI
Low complexity precoding for large millimeter wave MIMO systems
TL;DR: A precoding algorithm is developed that approximates the optimal unconstrained precoder using a low dimensional basis representation that can be efficiently implemented in RF hardware and allows mmWave systems to approach waterfilling capacity.
Book ChapterDOI
Sparse Spatio-spectral Representation for Hyperspectral Image Super-resolution
TL;DR: Comparison of the proposed approach with the state-of-the-art methods on both ground-based and remotely-sensed public hyperspectral image databases shows that the presented method achieves the lowest error rate on all test images in the three datasets.
Journal ArticleDOI
Fast global convergence of gradient methods for high-dimensional statistical recovery
TL;DR: The theory guarantees that projected gradient descent has a globally geometric rate of convergence up to the statistical precision of the model, meaning the typical distance between the true unknown parameter $\theta^*$ and an optimal solution $\hat{\theta}$.
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.