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Efficient compressive sensing with determinstic guarantees using expander graphs (2007)
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| Venue: | IEEE INFORMATION THEORY WORKSHOP |
| Citations: | 80 - 9 self |
BibTeX
@INPROCEEDINGS{Xu07efficientcompressive,
author = {Weiyu Xu and Babak Hassibi},
title = {Efficient compressive sensing with determinstic guarantees using expander graphs},
booktitle = {IEEE INFORMATION THEORY WORKSHOP},
year = {2007},
publisher = {}
}
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Abstract
Compressive sensing is an emerging technol-ogy which can recover a sparse signal vector of dimension n via a much smaller number of measurements than n. However, the existing compressive sensing methods may still suffer from relatively high recovery complexity, such as O(n3), or can only work efficiently when the signal is super sparse, sometimes without deterministic performance guarantees. In this paper, we propose a compressive sensing scheme with deterministic performance guarantees using expander-graphs-based measurement matrices and show that the signal recovery can be achieved with complexity O(n) even if the number of nonzero elements k grows linearly with n. We also investigate compressive sensing for approximately sparse signals using this new method. Moreover, explicit constructions of the considered expander graphs exist. Simulation results are given to show the performance and complexity of the new method.
Keyphrases
expander graph efficient compressive sensing determinstic guarantee new method deterministic performance guarantee high recovery complexity nonzero element simulation result abstract compressive sensing signal recovery sparse signal expander-graphs-based measurement matrix compressive sensing explicit construction compressive sensing scheme sparse signal vector super sparse
