End-to-End PET Image Reconstruction via a Posterior-Mean Diffusion Model

TL;DR

This work tackles the PET sinogram-to-PET reconstruction problem, where regression DL methods often blur details while posterior sampling methods risk artifacts. It introduces Posterior-Mean Denoising Diffusion Model (PMDM-PET), a two-stage approach that first learns an MMSE posterior-mean PET image from sinograms and then uses a conditional diffusion model to optimally transport that mean toward the ground-truth distribution under a perception constraint, grounded in the perception-distortion theory $D(0) = D^* + \min_{p_{\hat{\boldsymbol{x}}_0,\boldsymbol{x}_0^*}} \sum_t \mathrm{KL}(q(\hat{\boldsymbol{r}}_t|\hat{\boldsymbol{r}}_0,\boldsymbol{r}_0^*) \| p_\theta(\hat{\boldsymbol{r}}_t|\hat{\boldsymbol{r}}_{t+1},\boldsymbol{r}_0^*))$. The authors implement an MSE-trained $\boldsymbol{r}_0^*$ estimator (DeepPET) and a diffusion reverse process conditioned on $\boldsymbol{r}_0^*$, training with a denoising loss and evaluating on simulated BrainWeb data. They demonstrate that PMDM-PET yields higher PSNR and perceptual quality than five SOTA baselines, indicating a favorable distortion-perception tradeoff and potential clinical impact after further validation. Overall, the method advances PET reconstruction by jointly optimizing distortion and perceptual realism through a theoretically grounded, two-stage diffusion framework.

Abstract

Positron Emission Tomography (PET) is a functional imaging modality that enables the visualization of biochemical and physiological processes across various tissues. Recently, deep learning (DL)-based methods have demonstrated significant progress in directly mapping sinograms to PET images. However, regression-based DL models often yield overly smoothed reconstructions lacking of details (i.e., low distortion, low perceptual quality), whereas GAN-based and likelihood-based posterior sampling models tend to introduce undesirable artifacts in predictions (i.e., high distortion, high perceptual quality), limiting their clinical applicability. To achieve a robust perception-distortion tradeoff, we propose Posterior-Mean Denoising Diffusion Model (PMDM-PET), a novel approach that builds upon a recently established mathematical theory to explore the closed-form expression of perception-distortion function in diffusion model space for PET image reconstruction from sinograms. Specifically, PMDM-PET first obtained posterior-mean PET predictions under minimum mean square error (MSE), then optimally transports the distribution of them to the ground-truth PET images distribution. Experimental results demonstrate that PMDM-PET not only generates realistic PET images with possible minimum distortion and optimal perceptual quality but also outperforms five recent state-of-the-art (SOTA) DL baselines in both qualitative visual inspection and quantitative pixel-wise metrics PSNR (dB)/SSIM/NRMSE.

Figures (1)

• Figure 1: Qualitative comparison of PMDM-PET with Five Baselines on Three Example Slices. The first column shows the input sinogram images, and the second column shows the reference images reconstructed using OSEM algorithm. The third to seventh columns correspond to the five baselines (labeled above each image), and the final column shows the reconstructed PET images using our proposed PMDM-PET method. PSNR/SSIM values are reported below each slice, and squared error maps between each method and the reference image are also displayed (second, fourth and sixth rows).