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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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Robustly Stable Signal Recovery in Compressed Sensing With Structured Matrix Perturbation
Zai Yang,Cishen Zhang,Lihua Xie +2 more
TL;DR: Under mild conditions, it is shown that a sparse signal can be recovered by l1 minimization and the recovery error is at most proportional to the measurement noise level, which is similar to the standard CS result.
Journal ArticleDOI
Image compressive sensing recovery using adaptively learned sparsifying basis via L0 minimization
TL;DR: This paper proposes a new framework for image compressive sensing recovery using adaptively learned sparsifying basis via L0 minimization, and proposes a split Bregman iteration based technique to solve the non-convex L 0 minimization problem efficiently.
Journal ArticleDOI
Robust Visual Tracking Using Local Sparse Appearance Model and K-Selection
TL;DR: This work has developed a robust tracking algorithm using a local sparse appearance model (SPT) and a locally constrained sparse representation, called K-Selection, which has demonstrated better performance than alternatives reported in the recent literature.
Detection and estimation with compressive measurements
TL;DR: This paper aims to demonstrate the efforts towards in-situ applicability of EMMARM, as to provide real-time information about concrete mechanical properties such as E-modulus and compressive strength.
Journal ArticleDOI
Fault Diagnosis for a Wind Turbine Generator Bearing via Sparse Representation and Shift-Invariant K-SVD
TL;DR: A novel data-driven fault diagnosis method based on sparse representation and shift-invariant dictionary learning is proposed, which proves the effectiveness and robustness of the proposed method and the comparison with the state-of-the-art method is illustrated.
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.