One-bit compressed sensing with partial Gaussian circulant matrices

Sjoerd Dirksen; Hans Christian Jung; Holger Rauhut

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arXiv · 1710.03287

One-bit compressed sensing with partial Gaussian circulant matrices

Sjoerd Dirksen·Hans Christian Jung·Holger Rauhut

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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.

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Sjoerd Dirksen, Hans Christian Jung, Holger Rauhut. 2017-10-09. One-bit compressed sensing with partial Gaussian circulant matrices. https://arxiv.org/abs/1710.03287

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