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arXiv · 1911.11301

The recovery of complex sparse signals from few phaseless measurements

Yu Xia·Zhiqiang Xu
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Abstract

We study the stable recovery of complex $k$-sparse signals from as few phaseless measurements as possible. The main result is to show that one can employ $\ell_1$ minimization to stably recover complex $k$-sparse signals from $m\geq O(k\log (n/k))$ complex Gaussian random quadratic measurements with high probability. To do that, we establish that Gaussian random measurements satisfy the restricted isometry property over rank-$2$ and sparse matrices with high probability. This paper presents the first theoretical estimation of the measurement number for stably recovering complex sparse signals from complex Gaussian quadratic measurements.

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Yu Xia, Zhiqiang Xu. 2019-11-26. The recovery of complex sparse signals from few phaseless measurements. https://arxiv.org/abs/1911.11301

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