The Generalized Twin Image: Understanding Regularized Phase Retrieval
Abstract
Image priors can dramatically improve phase retrieval reconstruction, but their effectiveness strongly varies between imaging modalities. We introduce the generalized twin image, which extends the classical twin-image ambiguity from Fourier phase retrieval to any invertible sensing operator, to understand this effectiveness. The ambiguity extends to undersampled and oversampled measurements, remaining exact under undersampling and for oversampled coded Fourier measurements. We show that it provides a simple criterion to assess regularization effectiveness: the image prior should favor the ground truth over its generalized twin image. We propose the total-variation ratio as a simple measure of this preference, and derive closed-form estimates for structured random phase retrieval models. Experiments with a pretrained denoiser demonstrate that the ratio predicts regularized reconstruction performance across different sensing models.
Related
- Image Priors for Single-Shot Coded Diffraction Phase Retrieval
- A regularized lattice Boltzmann model for the solid-liquid phase change
- Generalized multi-energy model for computing radiation treatment parameters on image domain and automated model-selection framework
- Deterministic Ground-State Search in a Spatial Photonic Ising Machine by Phase Retrieval
- Phase Retrieval in ℂ4 Requires Exactly Eleven Measurements
BibTeX
@misc{hu2026generalized,
title = {{The Generalized Twin Image: Understanding Regularized Phase Retrieval}},
author = {Zhiyuan Hu and Michael Unser and Jonathan Dong},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41531},
eprint = {2610.41531},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41531},
}
RIS
TY - UNPB
TI - The Generalized Twin Image: Understanding Regularized Phase Retrieval
AU - Zhiyuan Hu
AU - Michael Unser
AU - Jonathan Dong
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41531
UR - https://arxiv.org/abs/2610.41531
AB - Image priors can dramatically improve phase retrieval reconstruction, but their effectiveness strongly varies between imaging modalities. We introduce the generalized twin image, which extends the classical twin-image ambiguity from Fourier phase retrieval to any invertible sensing operator, to understand this effectiveness. The ambiguity extends to undersampled and oversampled measurements, remaining exact under undersampling and for oversampled coded Fourier measurements. We show that it provides a simple criterion to assess regularization effectiveness: the image prior should favor the ground truth over its generalized twin image. We propose the total-variation ratio as a simple measure of this preference, and derive closed-form estimates for structured random phase retrieval models. Experiments with a pretrained denoiser demonstrate that the ratio predicts regularized reconstruction performance across different sensing models.
ER -