The recovery of complex sparse signals from few phaseless measurements

11/26/2019

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by   Yu Xia, et al.

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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 ℓ_1 minimization to stably recover complex k-sparse signals from m≥ O(klog (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.