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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Proceedings ArticleDOI
Adaptive Temporal Compressive Sensing for Video
Xin Yuan,Jianbo Yang,Patrick Llull,Xuejun Liao,Guillermo Sapiro,David J. Brady,Lawrence Carin +6 more
TL;DR: A CS algorithm to adapt the compression ratio based on the scene's temporal complexity, computed from the compressed data, without compromising the quality of the reconstructed video is proposed.
Journal ArticleDOI
Compressive sensing for cluster structured sparse signals: variational Bayes approach
TL;DR: This study is aiming to take into account the cluster structure property of sparse signals, of which the non-zero coefficients appear in clustered blocks, and proposes a non-parametric algorithm through variational Bayes approach to recover original sparse signals.
Journal ArticleDOI
SparseRI: A Compressed Sensing Framework for Aperture Synthesis Imaging in Radio Astronomy
TL;DR: This work presents a versatile CS-based image reconstruction framework called SparseRI, an interesting alternative to the CLEAN algorithm, which permits a wide choice of different regularizers for interferometric image reconstruction.
Journal ArticleDOI
Correntropy Matching Pursuit With Application to Robust Digit and Face Recognition
TL;DR: It is shown that CMP can adaptively assign small weights on severely corrupted entries of data and large weights on clean ones, thus reducing the effect of large noise, and to develop a robust sparse representation-based recognition method based on CMP.
Journal ArticleDOI
OMP based joint sparsity pattern recovery under communication constraints
TL;DR: This work explores the use of a shared multiple access channel (MAC) in forwarding observation vectors from each node to a fusion center and develops two efficient collaborative algorithms based on orthogonal matching pursuit (OMP) to jointly estimate the common sparsity pattern in a decentralized manner with a low communication overhead.
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.