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Fixed point method for PET reconstruction with learned plug-and-play regularization.

Marion Savanier1, Claude Comtat1, Florent Sureau1

  • 1BioMaps, Université Paris-Saclay, CEA, CNRS, Inserm, SHFJ, 91401 Orsay, France.

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|September 10, 2025
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Summary
This summary is machine-generated.

This study introduces a stable deep learning framework for Positron Emission Tomography (PET) image reconstruction. The Plug-and-Play (PnP) method enhances image quality and accuracy, especially with limited data.

Keywords:
image reconstructionmachine learningnuclear imagingoptimizationplug-and-play

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Area of Science:

  • Medical Imaging
  • Artificial Intelligence
  • Nuclear Medicine

Background:

  • Deep learning shows promise for medical image reconstruction, particularly in Positron Emission Tomography (PET).
  • Concerns exist regarding the stability and robustness of deep learning methods, especially with limited training data.
  • The Plug-and-Play (PnP) framework offers a potential solution to enhance PET reconstruction stability.

Purpose of the Study:

  • To explore the application of the Plug-and-Play (PnP) framework for stable and robust low-count Positron Emission Tomography (PET) reconstruction.
  • To evaluate the performance of different denoisers within the PnP framework, focusing on convergence properties and generalization capabilities.
  • To compare the proposed PnP algorithm against existing PET reconstruction techniques.

Main Methods:

  • Development of a convergent PnP algorithm for low-count PET reconstruction using the Douglas-Rachford splitting method.
  • Integration and evaluation of denoisers satisfying fixed-point conditions, including spectrally normalized networks and deep equilibrium models.
  • Assessment of bias-standard deviation trade-offs in clinically relevant regions and an unseen pathological case using synthetic and real PET data.

Main Results:

  • The proposed PnP method achieved lower bias than post-reconstruction denoising and reduced standard deviation at matched bias compared to model-based iterative reconstruction.
  • The deep equilibrium model denoiser demonstrated competitive performance and better generalization to unseen pathologies compared to convolutional networks.
  • The PnP approach with a deep equilibrium model showed more consistent generalization than an end-to-end unfolded network.

Conclusions:

  • The Plug-and-Play (PnP) framework holds significant potential for improving image quality and quantification accuracy in PET reconstruction.
  • Imposing specific convergence conditions on denoising networks is crucial for ensuring robust and generalizable performance in PET imaging.
  • Deep equilibrium models offer a promising direction for PnP-based PET reconstruction, balancing performance and generalization.