Journal ArticleDOI
The restricted isometry property and its implications for compressed sensing
TLDR
Candes et al. as discussed by the authors established new results about the accuracy of the reconstruction from undersampled measurements, which improved on earlier estimates, and have the advantage of being more elegant. But they did not consider the restricted isometry property of the sensing matrix.About:
This article is published in Comptes Rendus Mathematique.The article was published on 2008-05-01. It has received 3421 citations till now. The article focuses on the topics: Restricted isometry property & Compressed sensing.read more
Citations
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Journal ArticleDOI
CoSaMP: Iterative signal recovery from incomplete and inaccurate samples
Deanna Needell,Joel A. Tropp +1 more
TL;DR: A new iterative recovery algorithm called CoSaMP is described that delivers the same guarantees as the best optimization-based approaches and offers rigorous bounds on computational cost and storage.
Book
Understanding Machine Learning: From Theory To Algorithms
TL;DR: The aim of this textbook is to introduce machine learning, and the algorithmic paradigms it offers, in a principled way in an advanced undergraduate or beginning graduate course.
Journal ArticleDOI
CoSaMP: iterative signal recovery from incomplete and inaccurate samples
Deanna Needell,Joel A. Tropp +1 more
TL;DR: This extended abstract describes a recent algorithm, called, CoSaMP, that accomplishes the data recovery task and was the first known method to offer near-optimal guarantees on resource usage.
Journal ArticleDOI
Subspace Pursuit for Compressive Sensing Signal Reconstruction
Wei Dai,Olgica Milenkovic +1 more
TL;DR: The presented analysis shows that in the noiseless setting, the proposed algorithm can exactly reconstruct arbitrary sparse signals provided that the sensing matrix satisfies the restricted isometry property with a constant parameter.
BookDOI
Compressed sensing : theory and applications
Yonina C. Eldar,Gitta Kutyniok +1 more
TL;DR: In this paper, the authors introduce the concept of second generation sparse modeling and apply it to the problem of compressed sensing of analog signals, and propose a greedy algorithm for compressed sensing with high-dimensional geometry.
References
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Journal ArticleDOI
Decoding by linear programming
Emmanuel J. Candès,Terence Tao +1 more
TL;DR: F can be recovered exactly by solving a simple convex optimization problem (which one can recast as a linear program) and numerical experiments suggest that this recovery procedure works unreasonably well; f is recovered exactly even in situations where a significant fraction of the output is corrupted.
Journal ArticleDOI
Stable signal recovery from incomplete and inaccurate measurements
TL;DR: In this paper, the authors considered the problem of recovering a vector x ∈ R^m from incomplete and contaminated observations y = Ax ∈ e + e, where e is an error term.