Score-Based Generative Models for PET Image Reconstruction

TL;DR

This work adapts Score-Based Generative Models (SGMs) for PET image reconstruction, addressing Poisson noise and dynamic-range challenges via PET-specific normalisation and sampling strategies. It develops 2D-trained score models that can be applied to 3D PET data through slice-wise conditioning and enhanced 3D data-consistency steps, including DDS-based acceleration. The authors introduce MR-guided reconstruction using classifier-free guidance to leverage anatomical information from MR images, and compare several sampling schemes (Naive, DPS, DDS) against strong baselines on BrainWeb data, including out-of-distribution lesions. Results show that PET-DPS and PET-DDS offer robust performance with favorable PSNR, SSIM, and CRC metrics, with MR guidance yielding substantial gains in global image quality while raising considerations for local lesion detectability. The work opens avenues for principled uncertainty quantification and more principled non-negativity enforcement in PET SGMs, highlighting the potential for clinically impactful, robust PET reconstructions.

Abstract

Score-based generative models have demonstrated highly promising results for medical image reconstruction tasks in magnetic resonance imaging or computed tomography. However, their application to Positron Emission Tomography (PET) is still largely unexplored. PET image reconstruction involves a variety of challenges, including Poisson noise with high variance and a wide dynamic range. To address these challenges, we propose several PET-specific adaptations of score-based generative models. The proposed framework is developed for both 2D and 3D PET. In addition, we provide an extension to guided reconstruction using magnetic resonance images. We validate the approach through extensive 2D and 3D $\textit{in-silico}$ experiments with a model trained on patient-realistic data without lesions, and evaluate on data without lesions as well as out-of-distribution data with lesions. This demonstrates the proposed method's robustness and significant potential for improved PET reconstruction.

Figures (16)

• Figure 1: Schematic illustration of the modification for training and sampling steps of SGMs.
• Figure 2: Results for BrainWeb without lesions with noise level 2.5 for different penalty parameters. Standard deviation is across reconstructions from different realisations of measurements. The points represent different values of the parameter $\lambda$, and the notation ✙ and $\Diamondblack$ denote the smallest and largest value of $\lambda$, respectively.
• Figure 3: Results for BrainWeb with lesions with noise level 2.5 for different penalty parameters. Standard deviation is across reconstructions from different realisations of measurements. The points represent different values of the parameter $\lambda$, and the notation ✙ and $\Diamondblack$ denote the smallest and largest numerical value of $\lambda$, respectively.
• Figure 4: Comparisons of single slice reconstructions with the PET-DDS MR guided vs. unguided at noise level 2.5 without lesion (top) and with lesion (bottom).
• Figure 5: Results for 3D reconstruction using the FDG tracer for different penalty values. PET-DDS-RDP$_z$$\beta = 21.9$, and DIP+RDP $\beta=0.1$. Standard deviation is across reconstructions from different realisations of measurements. For DIP, the points corresponds to various number of optimisation steps. For the other methods, the points represent different values of the parameter $\lambda$, and the notation ✙ and $\Diamondblack$ denote the smallest and largest numerical value of $\lambda$, respectively.