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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
Perturbed Orthogonal Matching Pursuit
TL;DR: A novel perturbed orthogonal matching pursuit (POMP) algorithm that performs controlled perturbation of selected support vectors to decrease the Orthogonal residual at each iteration is presented.
Proceedings ArticleDOI
Kronecker product matrices for compressive sensing
TL;DR: This work proposes the use of Kronecker product matrices in CS to use such matrices as sparsifying bases that jointly model the different types of structure present in the signal.
Proceedings ArticleDOI
More with less: lowering user burden in mobile crowdsourcing through compressive sensing
TL;DR: This work presents Compressive CrowdSensing (CCS) -- a framework that enables compressive sensing techniques to be applied to mobile crowdsourcing scenarios and finds that it is able to outperform standard uses of compression sensing, as well as conventional approaches to lowering the quantity of user data needed by crowd systems.
Journal ArticleDOI
AMP-Net: Denoising based Deep Unfolding for Compressive Image Sensing
TL;DR: The proposed AMP-Net has better reconstruction accuracy than other state-of-the-art methods with high reconstruction speed and a small number of network parameters and is established by unfolding the iterative denoising process of the well-known approximate message passing algorithm.
Journal ArticleDOI
Sparse SAR imaging based on L 1/2 regularization
TL;DR: The new method is based on L1/2 regularization to reconstruct the scattering field, which optimizes a quadratic error term of the SAR observation process subject to the interested scene sparsity, and is more robust to the observation noise.
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.