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arXiv · 1604.04489

One-dimensional phase retrieval with additional interference measurements

Robert Beinert
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Abstract

The one-dimensional phase retrieval problem consists in the recovery of a complex-valued signal from its Fourier intensity. Due to the well-known ambiguousness of this problem, the determination of the original signal within the extensive solution set is challenging and can only be done under suitable a priori assumption or additional information about the unknown signal. Depending on the application, one has sometimes access to further interference measurements between the unknown signal and a reference signal. Beginning with the reconstruction in the discrete-time setting, we show that each signal can be uniquely recovered from its Fourier intensity and two further interference measurements between the unknown signal and a modulation of the signal itself. Afterwards, we consider the continuous-time problem, where we obtain an equivalent result. Moreover, the unique recovery of a continuous-time signal can also be ensured by using interference measurements with a known or an unknown reference which is unrelated to the unknown signal.

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Robert Beinert. 2016-04-15. One-dimensional phase retrieval with additional interference measurements. https://doi.org/10.1007/s00025-016-0633-9

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