Phase Retrieval from Coded Diffraction Patterns
Information Theory
2013-11-08 v2 Functional Analysis
math.IT
Numerical Analysis
Optimization and Control
Statistics Theory
Statistics Theory
Abstract
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.
Cite
@article{arxiv.1310.3240,
title = {Phase Retrieval from Coded Diffraction Patterns},
author = {Emmanuel Candes and Xiaodong Li and Mahdi Soltanolkotabi},
journal= {arXiv preprint arXiv:1310.3240},
year = {2013}
}