Solving ptychography with a convex relaxation

Ptychography is a powerful computational imaging technique that transforms a collection of low-resolution images into a high-resolution sample reconstruction. Unfortunately, algorithms that currently solve this reconstruction problem lack stability, robustness, and theoretical guarantees. Recently,...

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Bibliographic Details
Published in:New journal of physics 2015-05, Vol.17 (5), p.53044
Main Authors: Horstmeyer, Roarke, Chen, Richard Y, Ou, Xiaoze, Ames, Brendan, Tropp, Joel A, Yang, Changhuei
Format: Article
Language:English
Subjects:
Algorithms
coherent diffractive imaging
Computational geometry
Convexity
Image reconstruction
Image resolution
Mathematical models
Minima
Optimization
phase retrieval
Physics
Projection
ptychography
Reconstruction
Run time (computers)
Variance
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Summary:Ptychography is a powerful computational imaging technique that transforms a collection of low-resolution images into a high-resolution sample reconstruction. Unfortunately, algorithms that currently solve this reconstruction problem lack stability, robustness, and theoretical guarantees. Recently, convex optimization algorithms have improved the accuracy and reliability of several related reconstruction efforts. This paper proposes a convex formulation of the ptychography problem. This formulation has no local minima, it can be solved using a wide range of algorithms, it can incorporate appropriate noise models, and it can include multiple a priori constraints. The paper considers a specific algorithm, based on low-rank factorization, whose runtime and memory usage are near-linear in the size of the output image. Experiments demonstrate that this approach offers a 25% lower background variance on average than alternating projections, the ptychographic reconstruction algorithm that is currently in widespread use.
ISSN:1367-2630
1367-2630
DOI:10.1088/1367-2630/17/5/053044