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 intens...

Full description

Saved in:
Bibliographic Details
Published inApplied and computational harmonic analysis Vol. 39; no. 2; pp. 277 - 299
Main Authors Candès, Emmanuel J., Li, Xiaodong, Soltanolkotabi, Mahdi
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.09.2015
Subjects
Convex optimization
Diffraction
Fourier transform
Phase retrieval
Random matrix theory
Fourier transform
Diffraction
Random matrix theory
Convex optimization
Phase retrieval
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:1063-5203
1096-603X
DOI:10.1016/j.acha.2014.09.004