Phase Retrieval from Coded Diffraction Patterns

This paper considers the question 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 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. Numerical experiments with noiseless and noisy data complement our theoretical analysis and illustrate our approach.

• Publication year

  2013

• Venue

  arXiv: Information Theory

• Publication date

  2013-10-11

• Fields of study

  Mathematics, Physics, Computer Science

• Identifiers
  DOI 10.1016/J.ACHA.2014.09.004arXiv 1310.3240
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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