SONAR: A Physics-constrained Neural Representation for X-ray Dark-field CT

SAIMI 2026 Abstract · MIDL 2026 Short Paper · Full Paper Under Submission

Daniel Frey1,2, Theresa Hiu1,2, Julian McGinnis1,3,4, Paulina Bleuel1,2, Sofia Demianova1,2,3, Tina Dorosti1,2,3, Johannes B. Thalhammer1,2,3,5, Sebastian Peterhansl1,2, Zijin Huang1,2, Thomas Koehler5,6, Franz Pfeiffer1,2,3,6, Daniel Rueckert1,3,4,7, Florian Schaff1,2
1TUM   2MIBE   3TUM University Hospital   4MCML   5Philips   6IAS   7ICL
Short Paper Code
Conventional Phase Retrieval SONAR Phase Retrieval
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Conventional Phase Retrieval
SONAR

Talbot–Lau interferometry has enabled the first human-scale functional lung imaging on a clinical CT gantry. However, conventional reconstruction pipelines remain strongly limited by sparse phase information, leading to degraded projection quality and streak artifacts. We introduce SONAR ("Shot-Optimized Neural Adaptive Representation"), a physics-constrained neural phase retrieval framework for enhanced continuous-acquisition X-ray dark-field computed tomography.

The Physics: Talbot–Lau Interferometry

Talbot–Lau interferometry uses a grating-based setup to probe subtle X-ray interactions with matter. Integrated into a rotating CT gantry, it enables detection of small-angle scattering, which is highly sensitive to structural changes in lung tissue.

DFCT gantry Talbot–Lau principle

SONAR represents the scanned object as a continuous neural field that predicts X-ray interaction physics at arbitrary spatial coordinates. The representation is encoded directly through a differentiable forward model:

$$ y = T I + T IDV \cos(Φ + ϕ) $$

By embedding acquisition physics into the optimization process, the solution space is constrained to projections consistent with the recorded interferometric measurements.

The Representation: Continuous Neural Field

For each projection angle, the neural field is optimized to converge toward physically plausible solutions. We adopt a warm-start training scheme to leverages shared structure between neighboring projections for improved computational efficiency. Model weights are progressively refined over the full CT rotation. In effect, each projection is reconstructed from a local stack of adjacent shots within a defined angular window.


SONAR framework SONAR rotation

Projections obtained via conventional phase retrieval (sliding-window processing) are used as additional supervision signals to guide and stabilize training. We also incorporate a lightweight convolutional neural network to promote spatial image coherence.

Shots

Neural field solutions are penalized for deviations from recorded scans (shots or interferograms) at each acquisition angle. This ensures that the learned representation remains physically consistent with the measurements while enabling greater interpretability.

Projections

SONAR encodes a vector field representing the visibility reduction D, transmission T, and phase shift Φ in each detector pixel and for all acquisition angles. Operating in the projection domain reflects a conscious design choice to

(1)   decouple neural phase retrieval from tomographic reconstruction,
(2)   mitigate the risk of hallucinations in the reconstruction domain,
(3)   interpret the neural field as physical object encoding X-ray interaction physics.


Reconstructions

We evaluate SONAR against conventional sliding-window phase retrieval under continuous acquisition settings after tomographic reconstruction using the Feldkamp–Davis–Kress (FDK) algorithm. As ground truth (GT), we acquired consecutive multi-rotation scans at high dose and reconstructed the measurements via virtual phase stepping.

The reconstruction results demonstrate that SONAR

(1)   substantially reduces noise and reconstruction artifacts,
(2)   recovers structural features consistent with 20Ă— dose GT,
(3)   generalizes across unseen samples after scanner-specific initialization.

  

Dark-field

PSNR (3D): -- → --
SSIM (3D): -- → --

Attenuation


Differential Phase Contrast

Summary

SONAR enables per-instance self-supervised reconstruction without external pretraining, reducing susceptibility to data-driven hallucinations. By embedding X-ray physics directly into a neural field representation, it provides an interpretable and reliable extension of classical phase retrieval for DFCT.

These findings suggest that physics-constrained neural phase retrieval may help advance clinically viable human-scale dark-field CT.

BibTeX 


@article{frey2026sonar,
    title={SONAR: A Physics-constrained Neural Representation for X-ray Dark-field CT},
    author={Frey, Daniel and others},
    year={2026}
}

Acknowledgements

We thank all collaborators and supporting institutions involved in this work.

Financial support through the European Research Council (ERC Smart Detectors for Dark- field X-ray Imaging, SyG 101167328), and the Free State of Bavaria under the Excellence Strategy of the Federal Government and the States, as well as by the Technical University of Munich – Institute for Advanced Study.