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Wirtinger gradient descent methods for low-dose Poisson phase retrieval.
Inverse Probl. 40:125030 (2024)
The problem of phase retrieval has many applications in the field of optical imaging. Motivated by imaging experiments with biological specimens, we primarily consider the setting of low-dose illumination where Poisson noise plays the dominant role. In this paper, we discuss gradient descent algorithms based on different loss functions adapted to data affected by Poisson noise, in particular in the low-dose regime. Starting from the maximum log-likelihood function for the Poisson distribution, we investigate different regularizations and approximations of the problem to design an algorithm that meets the requirements that are faced in applications. In the course of this, we focus on low-count measurements. Based on an improved version of a variance-stabilizing transform for the Poisson distribution, we derive a decision rule for the regularization parameter in an averaged amplitude-based loss function. For all discussed loss functions, we study the convergence of the respective gradient descent algorithms to stationary points and find constant step sizes that guarantee descent of the loss in each iteration. Numerical experiments in the low-dose regime are performed to corroborate the theoretical observations.
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Publication type
Article: Journal article
Document type
Review
Keywords
Gradient Descent ; Low-dose Imaging ; Optimization ; Phase Retrieval ; Poisson Noise; Ptychography; Microscopy
ISSN (print) / ISBN
0266-5611
e-ISSN
1361-6420
Journal
Inverse Problems
Quellenangaben
Volume: 40,
Issue: 12,
Article Number: 125030
Publisher
Institute of Physics Publishing (IOP)
Publishing Place
Temple Circus, Temple Way, Bristol Bs1 6be, England
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Biological and Medical Imaging (IBMI)
Grants
German Research Foundation (DFG)
Helmholtz Association
Helmholtz Association