One-bit compressed sensing with partial Gaussian circulant matrices
Abstract
In this paper we consider memoryless one-bit compressed sensing with randomly subsampled Gaussian circulant matrices. We show that in a small sparsity regime and for small enough accuracy $\delta$, $m\sim \delta^{-4} s\log(N/s\delta)$ measurements suffice to reconstruct the direction of any $s$-sparse vector up to accuracy $\delta$ via an efficient program. We derive this result by proving that partial Gaussian circulant matrices satisfy an $\ell_1/\ell_2$ RIP-property. Under a slightly worse dependence on $\delta$, we establish stability with respect to approximate sparsity, as well as full vector recovery results.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2017
- DOI:
- 10.48550/arXiv.1710.03287
- arXiv:
- arXiv:1710.03287
- Bibcode:
- 2017arXiv171003287D
- Keywords:
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- Computer Science - Information Theory;
- Mathematics - Probability;
- 94A20;
- 60B20
- E-Print:
- 20 pages