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arXiv · 1410.7351

Fast Compressive Phase Retrieval from Fourier Measurements

Çağkan Yapar·Volker Pohl·Holger Boche
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Abstract

This paper considers the problem of recovering a $k$-sparse, $N$-dimensional complex signal from Fourier magnitude measurements. It proposes a Fourier optics setup such that signal recovery up to a global phase factor is possible with very high probability whenever $M \gtrsim 4k\log_2(N/k)$ random Fourier intensity measurements are available. The proposed algorithm is comprised of two stages: An algebraic phase retrieval stage and a compressive sensing step subsequent to it. Simulation results are provided to demonstrate the applicability of the algorithm for noiseless and noisy scenarios.

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Çağkan Yapar, Volker Pohl, Holger Boche. 2014-10-27. Fast Compressive Phase Retrieval from Fourier Measurements. https://arxiv.org/abs/1410.7351

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