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arXiv · 1605.07516

Robust phase retrieval with the swept approximate message passing (prSAMP) algorithm

Boshra Rajaei·Sylvain Gigan·Florent Krzakala·Laurent Daudet
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Abstract

In phase retrieval, the goal is to recover a complex signal from the magnitude of its linear measurements. While many well-known algorithms guarantee deterministic recovery of the unknown signal using i.i.d. random measurement matrices, they suffer serious convergence issues some ill-conditioned matrices. As an example, this happens in optical imagers using binary intensity-only spatial light modulators to shape the input wavefront. The problem of ill-conditioned measurement matrices has also been a topic of interest for compressed sensing researchers during the past decade. In this paper, using recent advances in generic compressed sensing, we propose a new phase retrieval algorithm that well-adopts for both Gaussian i.i.d. and binary matrices using both sparse and dense input signals. This algorithm is also robust to the strong noise levels found in some imaging applications.

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Boshra Rajaei, Sylvain Gigan, Florent Krzakala, Laurent Daudet. 2016-05-24. Robust phase retrieval with the swept approximate message passing (prSAMP) algorithm. https://doi.org/10.5201/ipol.2017.178

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