Published March 2012
| public
Book Section - Chapter
Projected ℓ_1-Minimization for Compressed Sensing
Abstract
We propose a new algorithm to recover a sparse signal from a system of linear measurements. By projecting the measured signal onto a properly chosen subspace, we can use the projection to zero in on a low-sparsity portion of our original signal, which we can recover using ℓ_1-minimization. We can then recover the remaining portion of our signal from an overdetermined system of linear equations. We prove that our scheme improves the threshold of ℓ_1-minimization, and we derive an upper bound for this new threshold. We support our theoretical results with numerical simulations which demonstrate that certain classes of signals come close to achieving this upper bound.
Additional Information
© 2012 IEEE. Date of Current Version: 30 August 2012. This work was supported in part by the National Science Foundation under grants CCF-0729203, CNS-0932428 and CCF-1018927, by the Office of Naval Research under the MURI grant N00014-08-1-0747, and by Caltech's Lee Center for Advanced Networking.Additional details
- Eprint ID
- 33920
- DOI
- 10.1109/ICASSP.2012.6288699
- Resolver ID
- CaltechAUTHORS:20120907-082737118
- NSF
- CCF-0729203
- NSF
- CNS-0932428
- NSF
- CCF-1018927
- Office of Naval Research (ONR)
- N00014-08-1-0747
- Caltech Lee Center for Advanced Networking
- Created
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2012-09-07Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field