The recovery of complex sparse signals from few phaseless measurements

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 $m\ge O(k\log (n/k))$ 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.

17 pages

References in corpus (1)

• Robust Compressive Phase Retrieval via L1 Minimization With Application to Image Reconstruction