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Joint Reconstruction of Activity and Attenuation in PET by Diffusion Posterior Sampling in Wavelet Coefficient Space

Clémentine Phung-Ngoc, Alexandre Bousse, Antoine De Paepe, Thibaut Merlin, Baptiste Laurent, Hong-Phuong Dang, Olivier Saut, Dimitris Visvikis

TL;DR

A joint reconstruction of activity and attenuation (JRAA) approach that eliminates the need for auxiliary anatomical imaging by relying solely on emission data and combines wavelet diffusion model (WDM) and diffusion posterior sampling (DPS) to reconstruct fully three-dimensional data.

Abstract

Attenuation correction (AC) is necessary for accurate activity quantification in positron emission tomography (PET). Conventional reconstruction methods typically rely on attenuation maps derived from a co-registered computed tomography (CT) or magnetic resonance imaging (MRI) scan. However, this additional scan may complicate the imaging workflow, introduce misalignment artifacts and increase radiation exposure. In this paper, we propose a joint reconstruction of activity and attenuation (JRAA) approach that eliminates the need for auxiliary anatomical imaging by relying solely on emission data. This framework combines wavelet diffusion model (WDM) and diffusion posterior sampling (DPS) to reconstruct fully three-dimensional (3-D) data. Experimental results show our method outperforms maximum likelihood activity and attenuation (MLAA) and MLAA with U-Net-based post processing, and yields high-quality noise-free reconstructions across various count settings when time-of-flight (TOF) information is available. It is also able to reconstruct non-TOF data, although the reconstruction quality significantly degrades in low-count (LC) conditions, limiting its practical effectiveness in such settings. Nonetheless, a non-TOF Biograph mMR data reconstruction with joint scatter estimation highlights the potential of the method for clinical applications. This approach represents a step towards stand-alone PET imaging by reducing the dependence on anatomical modalities while maintaining quantification accuracy, even in low-count scenarios when TOF information is available. Code will soon be available on GitHub at https://github.com/clemphg/jraa-dps.

Joint Reconstruction of Activity and Attenuation in PET by Diffusion Posterior Sampling in Wavelet Coefficient Space

TL;DR

A joint reconstruction of activity and attenuation (JRAA) approach that eliminates the need for auxiliary anatomical imaging by relying solely on emission data and combines wavelet diffusion model (WDM) and diffusion posterior sampling (DPS) to reconstruct fully three-dimensional data.

Abstract

Attenuation correction (AC) is necessary for accurate activity quantification in positron emission tomography (PET). Conventional reconstruction methods typically rely on attenuation maps derived from a co-registered computed tomography (CT) or magnetic resonance imaging (MRI) scan. However, this additional scan may complicate the imaging workflow, introduce misalignment artifacts and increase radiation exposure. In this paper, we propose a joint reconstruction of activity and attenuation (JRAA) approach that eliminates the need for auxiliary anatomical imaging by relying solely on emission data. This framework combines wavelet diffusion model (WDM) and diffusion posterior sampling (DPS) to reconstruct fully three-dimensional (3-D) data. Experimental results show our method outperforms maximum likelihood activity and attenuation (MLAA) and MLAA with U-Net-based post processing, and yields high-quality noise-free reconstructions across various count settings when time-of-flight (TOF) information is available. It is also able to reconstruct non-TOF data, although the reconstruction quality significantly degrades in low-count (LC) conditions, limiting its practical effectiveness in such settings. Nonetheless, a non-TOF Biograph mMR data reconstruction with joint scatter estimation highlights the potential of the method for clinical applications. This approach represents a step towards stand-alone PET imaging by reducing the dependence on anatomical modalities while maintaining quantification accuracy, even in low-count scenarios when TOF information is available. Code will soon be available on GitHub at https://github.com/clemphg/jraa-dps.

Paper Structure

This paper contains 22 sections, 23 equations, 8 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background on Joint Activity and Attenuation Reconstruction
  3. PET Reconstruction with Known Attenuation
  4. Joint PET Activity and Attenuation Reconstruction
  5. Proposed Approach: Joint Reconstruction of the Activity and the Attenuation by Diffusion Posterior Sampling
  6. Diffusion Models
  7. Diffusion Posterior Sampling
  8. Joint Scatter Estimation
  9. Summary
  10. Experiments
  11. Patient Data Images
  12. Model Training
  13. Methods for Comparison
  14. Experiment 1---Simulated Raw Data
  15. Raw Data Simulation
  16. ...and 7 more sections

Figures (8)

  • Figure 1: Proposed reconstruction framework for JRAA-DPS. A WDM is trained to generate activity-attenuation image pairs and DPS is employed to reconstruct from measurements. Joint scatter estimation can be integrated into the framework.
  • Figure 2: Experiment 1---Reconstructions in HC setting with relative difference with respect to the reference images.
  • Figure 3: Experiment 1---Reconstructions in LC setting with relative difference with respect to the reference images.
  • Figure 4: Experiment 1---SSIM against PSNR plots for 30 test reconstructions.
  • Figure 5: Experiment 1---Bias against STD for different values of the hyper-parameters (cf. Section \ref{['sec:quantanal']}). All reconstructions use TOF information.
  • ...and 3 more figures