Journal
SIAM REVIEW
Volume 57, Issue 2, Pages 225-251Publisher
SIAM PUBLICATIONS
DOI: 10.1137/151005099
Keywords
diffraction; Fourier transform; convex optimization; trace-norm minimization
Categories
Funding
- NSF [CCF-0963835, DMS 0811169, DMS-1042939]
- Waterman Award
- Israel Science Foundation [170/10]
- DARPA [N66001-11-1-4090]
- Department of Defense (DoD) through the National Defense Science and Engineering Graduate (NDSEG) Fellowship Program
Ask authors/readers for more resources
This paper develops a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging, and many other applications. Our approach, called PhaseLift, combines multiple structured illuminations together with ideas from convex programming to recover the phase from intensity measurements, typically from the modulus of the diffracted wave. We demonstrate empirically that a complex-valued object can be recovered from the knowledge of the magnitude of just a few diffracted patterns by solving a simple convex optimization problem inspired by the recent literature on matrix completion. More importantly, we also demonstrate that our noise-aware algorithms are stable in the sense that the reconstruction degrades gracefully as the signal-to-noise ratio decreases. Finally, we introduce some theory showing that one can design very simple structured illumination patterns such that three diffracted figures uniquely determine the phase of the object we wish to recover.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available