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
Polarimetric Contextual Classification of PolSAR Images Using Sparse Representation and Superpixels
Jilan Feng,Zongjie Cao,Yiming Pi +2 more
TL;DR: It is proven that the classification performance of polarimetric synthetic aperture radar images is improved by using contextual information by combining sparsity-based classification methods with the concept of superpixels.
Proceedings ArticleDOI
Non-adaptive group testing: Explicit bounds and novel algorithms
TL;DR: Inspired by compressive sensing algorithms, four novel computationally efficient decoding algorithms for group testing are introduced, CBP via Linear Programming (CBP-LP), NCBP- LP (Noisy CBP-LP, and the two related algorithmsNCBP-SLP+ and NCBP -SLP- (“Simple” NC BP-LP).
Fast Bayesian Matching Pursuit: Model Uncertainty and Parameter Estimation for Sparse Linear Models
Philip Schniter,Justin Ziniel +1 more
TL;DR: A low-complexity recursive procedure is presented for model selection and minimum mean squared error (MMSE) estimation in linear regression and returns both a set of high posterior probability models and an approximate MMSE estimate of the parameter vector.
Landmark recognition with sparse representationclassification and extreme learning machine
TL;DR: In this paper, a novel landmark recognition algorithm using the spatial pyramid kernel based bag-of-words (SPK-BoW) histogram approach with the feedforward artificial neural networks (FNN) and the sparse representation classifier (SRC) was proposed.
Journal ArticleDOI
Compressed-Sensed-Domain L 1 -PCA Video Surveillance
Ying Liu,Dimitris A. Pados +1 more
TL;DR: The proposed L1-norm procedure directly carries out low-rank background representation without reconstructing the video sequence and, at the same time, exhibits significant robustness against outliers in CS measurements compared to L2-norm PCA.
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.