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
Compressive sensing for subsurface imaging using ground penetrating radar
TL;DR: A novel data acquisition system for wideband synthetic aperture imaging based on CS by exploiting sparseness of point-like targets in the image space by using linear projections of the returned signals with random vectors as measurements.
Posted Content
Millimeter Wave Beam-Selection Using Out-of-Band Spatial Information
TL;DR: In this paper, the authors proposed to use spatial information extracted at sub-6 GHz to help establish the mmWave link, which can reduce the training overhead of in-band only beam-selection by 4x.
Journal ArticleDOI
Stability Results for Random Sampling of Sparse Trigonometric Polynomials
TL;DR: In this article, it was shown that recovery by a BP variant is stable under perturbation of the samples values by noise and a similar partial result for OMP is provided.
Journal ArticleDOI
Distributed Compressed Estimation Based on Compressive Sensing
TL;DR: Simulations for a wireless sensor network illustrate the advantages of the proposed scheme and algorithm in terms of convergence rate and mean square error performance.
Proceedings ArticleDOI
On optimization of the measurement matrix for compressive sensing
TL;DR: A gradient descent method is proposed to optimize the measurement matrix and is designed to minimize the mutual coherence which is described as absolute off-diagonal elements of the corresponding Gram matrix.
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.