Efficient near-field ptychography reconstruction using the Hessian operator
(2025) In Optics Express 33(14). p.30543-30568- Abstract
X-ray ptychography is a powerful and robust coherent imaging method providing access to the complex object and probe (illumination). Ptychography reconstruction is typically performed using first-order methods due to their computational efficiency. Higher-order methods, while potentially more accurate, are often prohibitively expensive in terms of computation. In this study, we present a mathematical framework for reconstruction using second-order information derived from an efficient computation of the bilinear Hessian and Hessian operator. The formulation is provided for Gaussian-based models, enabling the simultaneous reconstruction of the object, probe, and object positions. Synthetic data tests, along with experimental near-field... (More)
X-ray ptychography is a powerful and robust coherent imaging method providing access to the complex object and probe (illumination). Ptychography reconstruction is typically performed using first-order methods due to their computational efficiency. Higher-order methods, while potentially more accurate, are often prohibitively expensive in terms of computation. In this study, we present a mathematical framework for reconstruction using second-order information derived from an efficient computation of the bilinear Hessian and Hessian operator. The formulation is provided for Gaussian-based models, enabling the simultaneous reconstruction of the object, probe, and object positions. Synthetic data tests, along with experimental near-field ptychography data processing, demonstrate a ten-fold reduction in computation time compared to first-order methods. The derived formulas for computing the Hessians, along with the strategies for incorporating them into optimization schemes, are well-structured and easily adaptable to various ptychography problem formulations.
(Less)
- author
- Carlsson, Marcus LU ; Wendt, Herwig ; Cloetens, Peter and Nikitin, Viktor LU
- organization
- publishing date
- 2025-07-14
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Optics Express
- volume
- 33
- issue
- 14
- pages
- 26 pages
- publisher
- Optical Society of America
- external identifiers
-
- pmid:40734148
- scopus:105011586446
- ISSN
- 1094-4087
- DOI
- 10.1364/OE.561856
- language
- English
- LU publication?
- yes
- additional info
- Publisher Copyright: © 2025 Optica Publishing Group (formerly OSA). All rights reserved.
- id
- c62c91b2-fda9-4d31-b125-fe3626230ebe
- date added to LUP
- 2025-12-11 08:58:05
- date last changed
- 2025-12-11 08:58:49
@article{c62c91b2-fda9-4d31-b125-fe3626230ebe,
abstract = {{<p>X-ray ptychography is a powerful and robust coherent imaging method providing access to the complex object and probe (illumination). Ptychography reconstruction is typically performed using first-order methods due to their computational efficiency. Higher-order methods, while potentially more accurate, are often prohibitively expensive in terms of computation. In this study, we present a mathematical framework for reconstruction using second-order information derived from an efficient computation of the bilinear Hessian and Hessian operator. The formulation is provided for Gaussian-based models, enabling the simultaneous reconstruction of the object, probe, and object positions. Synthetic data tests, along with experimental near-field ptychography data processing, demonstrate a ten-fold reduction in computation time compared to first-order methods. The derived formulas for computing the Hessians, along with the strategies for incorporating them into optimization schemes, are well-structured and easily adaptable to various ptychography problem formulations.</p>}},
author = {{Carlsson, Marcus and Wendt, Herwig and Cloetens, Peter and Nikitin, Viktor}},
issn = {{1094-4087}},
language = {{eng}},
month = {{07}},
number = {{14}},
pages = {{30543--30568}},
publisher = {{Optical Society of America}},
series = {{Optics Express}},
title = {{Efficient near-field ptychography reconstruction using the Hessian operator}},
url = {{http://dx.doi.org/10.1364/OE.561856}},
doi = {{10.1364/OE.561856}},
volume = {{33}},
year = {{2025}},
}