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
Channel Estimation for OFDM Systems over Doubly Selective Channels: A Distributed Compressive Sensing Based Approach
TL;DR: This paper transforms the original DS channel into a novel two-dimensional channel model, taking advantage of the basis expansion model (BEM) and the channel sparsity in the delay domain, and designs a special decoupling form originating from a novel sparse pilot pattern for estimation.
Journal ArticleDOI
A stepwise regression method and consistent model selection for high-dimensional sparse linear models
Ching-Kang Ing,Tze Leung Lai +1 more
TL;DR: The orthogonal greedy algorithm is introduced and the resultant regression estimate is shown to have the oracle property of being equivalent to least squares regression on an asymptotically minimal set of relevant regressors under a strong sparsity condition.
Proceedings ArticleDOI
Active user detection and channel estimation in uplink CRAN systems
TL;DR: A modified Bayesian compressive sensing (BCS) algorithm is proposed to conduct AUD and CE in CRAN, which exploits not only the active user sparsity, but also the innate heterogeneous path loss effects and the joint sparsity structures in multi-antenna uplink CRAN systems.
Journal ArticleDOI
Class-Dependent Sparse Representation Classifier for Robust Hyperspectral Image Classification
Minshan Cui,Saurabh Prasad +1 more
TL;DR: Class-dependent sparse representation classifier (cdSRC) is proposed for hyperspectral image classification, which effectively combines the ideas of SRC and K-nearest neighbor classifier in a classwise manner to exploit both correlation and Euclidean distance relationship between test and training samples.
Journal ArticleDOI
Vehicle Detection in High-Resolution Aerial Images via Sparse Representation and Superpixels
Ziyi Chen,Cheng Wang,Chenglu Wen,Xiuhua Teng,Yiping Chen,Haiyan Guan,Huan Luo,Liujuan Cao,Jonathan Li +8 more
TL;DR: A superpixel segmentation method designed for aerial images is proposed to control the segmentation with a low breakage rate and obtain a dictionary with high discrimination ability for vehicle detection from high-resolution aerial images.
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.