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Phase retrieval using the Hessian operator

Carlsson, Marcus LU ; Nikitin, Viktor LU and Wendt, Herwig (2025) 2025 IEEE Statistical Signal Processing Workshop, SSP 2025 In IEEE Workshop on Statistical Signal Processing Proceedings p.46-50
Abstract

Phase retrieval is a fundamental problem in optics, particularly in ptychography, where reconstructing an unknown wavefield from intensity-only measurements poses significant computational challenges. In this work, we introduce a novel phase retrieval method using the bilinear Hessian and Hessian operator to improve optimization efficiency. By formulating the problem in a differential calculus framework over linear spaces, we derive gradient and Hessian expressions without explicitly differentiating, enabling efficient second-order based solvers. This enables to implement and analyze conjugate gradient, quasi-Newton, and gradient descent methods with Newton step size, demonstrating a one-order-of-magnitude improvement in convergence... (More)

Phase retrieval is a fundamental problem in optics, particularly in ptychography, where reconstructing an unknown wavefield from intensity-only measurements poses significant computational challenges. In this work, we introduce a novel phase retrieval method using the bilinear Hessian and Hessian operator to improve optimization efficiency. By formulating the problem in a differential calculus framework over linear spaces, we derive gradient and Hessian expressions without explicitly differentiating, enabling efficient second-order based solvers. This enables to implement and analyze conjugate gradient, quasi-Newton, and gradient descent methods with Newton step size, demonstrating a one-order-of-magnitude improvement in convergence speed compared to traditional approaches. Numerical experiments on near-field ptychography data validate the method's robustness and computational efficiency. Our approach significantly reduces reconstruction time, making it highly relevant for real-time imaging applications, such as in-situ experiments.

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Please use this url to cite or link to this publication:
author
; and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
bilinear Hessian, Hessian operator, Newton step, Phase retrieval, Second order optimization
host publication
2025 IEEE Statistical Signal Processing Workshop, SSP 2025
series title
IEEE Workshop on Statistical Signal Processing Proceedings
pages
5 pages
publisher
IEEE Computer Society
conference name
2025 IEEE Statistical Signal Processing Workshop, SSP 2025
conference location
Edinburgh, United Kingdom
conference dates
2025-06-08 - 2025-06-11
external identifiers
  • scopus:105012172222
ISSN
2373-0803
2693-3551
ISBN
9798331518004
DOI
10.1109/SSP64130.2025.11073275
language
English
LU publication?
yes
additional info
Publisher Copyright: © 2025 IEEE.
id
ab63d57d-f88e-4623-86a7-4b7b47e40075
date added to LUP
2026-01-13 13:19:13
date last changed
2026-01-13 13:20:17
@inproceedings{ab63d57d-f88e-4623-86a7-4b7b47e40075,
  abstract     = {{<p>Phase retrieval is a fundamental problem in optics, particularly in ptychography, where reconstructing an unknown wavefield from intensity-only measurements poses significant computational challenges. In this work, we introduce a novel phase retrieval method using the bilinear Hessian and Hessian operator to improve optimization efficiency. By formulating the problem in a differential calculus framework over linear spaces, we derive gradient and Hessian expressions without explicitly differentiating, enabling efficient second-order based solvers. This enables to implement and analyze conjugate gradient, quasi-Newton, and gradient descent methods with Newton step size, demonstrating a one-order-of-magnitude improvement in convergence speed compared to traditional approaches. Numerical experiments on near-field ptychography data validate the method's robustness and computational efficiency. Our approach significantly reduces reconstruction time, making it highly relevant for real-time imaging applications, such as in-situ experiments.</p>}},
  author       = {{Carlsson, Marcus and Nikitin, Viktor and Wendt, Herwig}},
  booktitle    = {{2025 IEEE Statistical Signal Processing Workshop, SSP 2025}},
  isbn         = {{9798331518004}},
  issn         = {{2373-0803}},
  keywords     = {{bilinear Hessian; Hessian operator; Newton step; Phase retrieval; Second order optimization}},
  language     = {{eng}},
  pages        = {{46--50}},
  publisher    = {{IEEE Computer Society}},
  series       = {{IEEE Workshop on Statistical Signal Processing Proceedings}},
  title        = {{Phase retrieval using the Hessian operator}},
  url          = {{http://dx.doi.org/10.1109/SSP64130.2025.11073275}},
  doi          = {{10.1109/SSP64130.2025.11073275}},
  year         = {{2025}},
}