Published 2012
| Published
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Fundamental thresholds in compressed sensing: a high-dimensional geometry approach
- Creators
- Xu, Weiyu
- Hassibi, Babak
- Others:
- Eldar, Yonina C.
- Kutyniok, Gitta
Abstract
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.
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.Attached Files
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Additional details
- Eprint ID
- 35324
- Resolver ID
- CaltechAUTHORS:20121107-095923799
- NSF
- CCF-0729203
- David and Lucile Packard Foundation
- Caltech Lee Center for Advanced Networking
- Created
-
2012-11-09Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field