Robert Beinert coauthored an account of Fourier phase retrieval with Tamir Bendory and Yonina C. Eldar. Their analysis separates uniqueness questions from reconstruction algorithms and records the symmetries invisible to Fourier-magnitude measurements. This clarifies why an algorithm producing a signal is insufficient unless the measurement design also makes the signal identifiable.[ref]
Fourier Phase Retrieval: Uniqueness and Algorithms by Tamir Bendory and others. Introduction and Section 3.1
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