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.
Shannon, Communication in the presence of noise, Proceedings Institute of Radio Engineers, 37 (1949) 10–21
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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.