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
Recent Advances on Spectral–Spatial Hyperspectral Image Classification: An Overview and New Guidelines
TL;DR: A concept of spatial dependency system that involves pixel dependency and label dependency, with two main factors: neighborhood covering and neighborhood importance is developed, and several representative spectral–spatial classification methods are applied on real-world hyperspectral data.
Posted Content
Bayesian Compressive Sensing via Belief Propagation
TL;DR: This work performs asymptotically optimal Bayesian inference using belief propagation (BP) decoding, which represents the CS encoding matrix as a graphical model, and focuses on a two-state mixture Gaussian model that is easily adapted to other signal models.
Proceedings ArticleDOI
Theory and Implementation of an Analog-to-Information Converter using Random Demodulation
TL;DR: The new theory of compressive sensing enables direct analog-to-information conversion of compressible signals at sub-Nyquist acquisition rates and proves the concept under the effect of circuit nonidealities.
Journal ArticleDOI
Multitask Compressive Sensing
TL;DR: It has been demonstrated that with appropriate design of the compressive measurements used to define v, the decompressive mapping vrarru may be performed with error with asymptotic properties analogous to those of the best adaptive transform-coding algorithm applied in the basis Psi.
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Learning with Structured Sparsity
TL;DR: This paper investigates a new learning formulation called structured sparsity, which is a natural extension of the standard sparsity concept in statistical learning and compressive sensing by allowing arbitrary structures on the feature set, which generalizes the group sparsity idea.
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.