Phase Retrieval: Uniqueness and Stability

  title={Phase Retrieval: Uniqueness and Stability},
  author={Philipp Grohs and Sarah Koppensteiner and Martin Rathmair},
  journal={SIAM Rev.},
The problem of phase retrieval, i.e., the problem of recovering a function from the magnitudes of its Fourier transform, naturally arises in various fields of physics, such as astronomy, radar, speech recognition, quantum mechanics and, perhaps most prominently, diffraction imaging. The mathematical study of phase retrieval problems possesses a long history with a number of beautiful and deep results drawing from different mathematical fields, such as harmonic analyis, complex analysis, or… 

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