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
Joint Wall Mitigation and Compressive Sensing for Indoor Image Reconstruction
TL;DR: This paper enables joint wall clutter mitigation and CS application using a reduced set of spatial-frequency observations in stepped frequency radar platforms and demonstrates that wall mitigation techniques, such as spatial filtering and subspace projection, can proceed using fewer measurements.
Posted Content
On-off random access channels: A compressed sensing framework
TL;DR: A new algorithm, called sequential OMP, is presented that illustrates that iterative detection combined with power ordering or power shaping can significantly improve the high SNR performance and provides insight into the roles of power control and multiuser detection on random-access signalling.
Journal ArticleDOI
Sparsity Averaging for Compressive Imaging
TL;DR: A novel sparsity prior for compressive imaging in the context of the theory of compressed sensing with coherent redundant dictionaries is discussed, based on the observation that natural images exhibit strong average sparsity over multiple coherent frames.
Journal ArticleDOI
Forward–Backward Greedy Algorithms for Atomic Norm Regularization
TL;DR: This paper describes an optimization algorithm called CoGEnT that produces solutions with succinct atomic representations for reconstruction problems, generally formulated with atomic-norm constraints, and introduces several novel applications that are enabled by the atomic- norm framework.
Proceedings ArticleDOI
High performance compressive sensing reconstruction hardware with QRD process
TL;DR: A high performance architecture for the reconstruction of compressive sampled signals using Orthogonal Matching Pursuit (OMP) algorithm and a new algorithm for finding fast inverse square root of a fixed point number is implemented to support the QRD process.
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.