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Considering the ambiguousness of the discrete-time phase retrieval problem torecover a signal from its Fourier intensities, one can ask the question: whatadditional information about the unknown signal do we need to select thecorrect solution within the large solution set? Based on a characterization ofthe occurring ambiguities, we investigate different a priori conditions inorder to reduce the number of ambiguities or even to receive a unique solution.Particularly, if we have access to additional magnitudes of the unknown signalin the time domain, we can show that almost all signals with finite support canbe uniquely recovered. Moreover, we prove that an analogous result can beobtained by exploiting additional phase information.

Enforcing uniqueness in one-dimensional phase retrieval by additional signal information in time domain