Fixed point method for PET reconstruction with plug-and-play regularization
Résumé
Deep learning has shown great promise for improving medical image reconstruction, often surpassing traditional model-based iterative methods. However, concerns remain about the stability and robustness of these approaches, particularly when trained on limited data. The Plug-and-Play framework offers a promising solution, showing that a convergent and robust reconstruction can be ensured, provided conditions on the plugged network. Yet, it has been underexplored in PET reconstruction.
This paper introduces a convergent PnP algorithm for low-count PET reconstruction, leveraging the Douglas-Rachford splitting method and various networks trained on the fixed point conditions. We evaluate bias-standard deviation tradeoffs across multiple regions including an unseen pathological case and compared to model-based iterative reconstruction, post-reconstruction processing, and PnP with a Gaussian denoiser. Our findings emphasize the importance of how convergence conditions are imposed on the PnP networks. While spectral normalization underperformed, our deep equilibrium model remained competitive with convolutional architectures and generalized better on our unseen pathology. Our method achieved lower bias than post-reconstruction processing and reduced standard deviation at matched bias compared to model-based iterative reconstruction. Our results demonstrate PnP's potential to improve image quality and quantification accuracy in PET reconstruction.
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