Open Access
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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Target Dictionary Construction-Based Sparse Representation Hyperspectral Target Detection Methods
Dehui Zhu,Bo Du,Liangpei Zhang +2 more
TL;DR: A target dictionary construction-based method is constructed, then a constructed target dictionary-based sparsity-based target detection model and the constructed target Dictionary-based sparse representation-based binary hypothesis model are proposed, which are called TDC-STD and T DC-SRBBH, respectively.
Journal ArticleDOI
Hardware Performance Counter-Based Malware Identification and Detection with Adaptive Compressive Sensing
TL;DR: This work presents a “sample-locally-analyze-remotely” technique to reduce the overhead in the monitored system which has limited storage and computing resources, and demonstrates an 80% I/O bandwidth reduction after applying Compressive Sensing.
Journal ArticleDOI
Exploiting Structured Sparsity for Hyperspectral Anomaly Detection
TL;DR: A novel hyperspectral AD method is presented, which can exploit the structured sparsity in modeling the background more accurately and outperforms several state-of-the-art hyperspectrals AD methods.
Journal ArticleDOI
Robust compressive sensing of sparse signals: a review
TL;DR: Robust nonlinear reconstruction strategies for sparse signals based on replacing the commonly used ℓ2 norm by M-estimators as data fidelity functions are overviewed, offering a robust framework for CS.
Journal ArticleDOI
On the choice of Compressed Sensing priors and sparsifying transforms for MR image reconstruction: An experimental study
Angshul Majumdar,Rabab K. Ward +1 more
TL;DR: This work will review and evaluate the popular MR image reconstruction techniques and show that analysis prior with complex dualtree wavelets yields the best reconstruction results.
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.