For real-valued objects, iterative phase retrieval can recover both the object and the missing intensity values when the missing fraction stays below 1 - 2/sigma^2 for diffraction patterns and 1 - 1/sigma^2 for holograms.
Kotelnikov, On the transmission capacity of "ether" and wire in electrocommunications, Proc
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Reconstruction of missing information in diffraction patterns and holograms by iterative phase retrieval
For real-valued objects, iterative phase retrieval can recover both the object and the missing intensity values when the missing fraction stays below 1 - 2/sigma^2 for diffraction patterns and 1 - 1/sigma^2 for holograms.