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Fundamental thresholds in compressed sensing: a high-dimensional geometry approach

Xu, Weiyu and Hassibi, Babak (2012) Fundamental thresholds in compressed sensing: a high-dimensional geometry approach. In: Compressed Sensing: Theory and Applications. Cambridge University Press , Cambridge, pp. 305-347. ISBN 1-107-00558-2.

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In this chapter, we introduce a unified high-dimensional geometric framework for analyzing the phase transition phenomenon of ℓ_1 minimization in compressive sensing. This framework connects studying the phase transitions of ℓ_1 minimization with computing the Grassmann angles in high-dimensional convex geometry. We demonstrate the broad applications of this Grassmann angle framework by giving sharp phase transitions for ℓ_1 minimization recovery robustness, weighted ℓ_1 minimization algorithms, and iterative reweighted ℓ_1 minimization algorithms.

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Additional Information:© 2012 Cambridge University Press. This work was supported in part by the National Science Foundation under grant no. CCF-0729203, by the David and Lucille Packard Foundation, and by Caltech's Lee Center for Advanced Networking.
Funding AgencyGrant Number
David and Lucile Packard FoundationUNSPECIFIED
Caltech Lee Center for Advanced NetworkingUNSPECIFIED
Subject Keywords:Engineering, Communications and signal processing, Computer graphics, image processing, robotics and computer vision
Record Number:CaltechAUTHORS:20121107-095923799
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Official Citation:Eldar, Yonina C.; and Kutyniok, Gitta. Compressed Sensing. Cambridge University Press, 2012. Cambridge Books Online.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:35324
Deposited By: Tony Diaz
Deposited On:09 Nov 2012 00:36
Last Modified:09 Nov 2021 23:14

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