Phase Retrieval from Coded Diffraction Patterns

Phase Retrieval is the problem of recovering the phase of an object from intensity-only measurements, a problem which naturally appears in X-ray crystallography and related disciplines. We study a physically realistic setup (depicted below) where one can modulate the signal of interest and then collect the intensity of its diffraction pattern, each modulation thereby producing a sort of coded diffraction pattern. We show that PhaseLift, a recent convex programming technique, recovers the phase information exactly from a number of random modulations, which is polylogarithmic in the number of unknowns. This webpage provides the code for numerical experiments with noiseless and noisy data that complement our theoretical analysis and illustrate our approach.

• Phase Retrieval from Coded Diffraction Patterns. E. J. Candes, X. Li and M. Soltanolkotabi.