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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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A Data-Driven Sparse GLM for fMRI Analysis Using Sparse Dictionary Learning With MDL Criterion
TL;DR: A new data driven fMRI analysis that is derived solely based upon the sparsity of the signals is proposed that enables estimation of spatially adaptive design matrix as well as sparse signal components that represent synchronous, functionally organized and integrated neural hemodynamics.
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Pattern-Coupled Sparse Bayesian Learning for Recovery of Block-Sparse Signals
TL;DR: A new sparse Bayesian learning method for recovery of block-sparse signals with unknown cluster patterns by introducing a pattern-coupled hierarchical Gaussian prior to characterize the pattern dependencies among neighboring coefficients, where a set of hyperparameters are employed to control the sparsity of signal coefficients.
Journal ArticleDOI
Energy-Efficient Sensing in Wireless Sensor Networks Using Compressed Sensing
TL;DR: It is shown that, for some applications, compressed sensing and distributed compressed sensing can provide greater energy efficiency than transform coding and model-based adaptive sensing in wireless sensor networks.
Journal ArticleDOI
Remotely Sensed Image Classification Using Sparse Representations of Morphological Attribute Profiles
Benqin Song,Jun Li,Mauro Dalla Mura,Peijun Li,Antonio Plaza,Jose M. Bioucas-Dias,Jon Atli Benediktsson,Jocelyn Chanussot +7 more
TL;DR: This paper uses extended multiattribute profiles (EMAPs) to integrate the spatial and spectral information contained in the data to exploit the inherent low-dimensional structure of the EMAPs to provide state-of-the-art classification results for different multi/hyperspectral data sets.
Journal ArticleDOI
Coordinate descent optimization for l 1 minimization with application to compressed sensing; a greedy algorithm
Yingying Li,Stanley Osher +1 more
TL;DR: This work proposes a fast algorithm for solving the Basis Pursuit problem, min u, and claims that in combination with a Bregman iterative method, this algorithm will achieve a solution with speed and accuracy competitive with some of the leading methods for the basis pursuit problem.
References
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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.