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

arXiv: https://arxiv.org/abs/2503.08546 · HTML: https://mlsanity.com/paper/2503.08546/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 13 of its 21 references that are in the map.
- First posted on arXiv 11 Mar 2025.

## Placed in

- Diffusion models / [Medical imaging and segmentation](https://mlsanity.com/diffusion/medical-imaging-and-segmentation/)

## Builds on (most cited first, 13 of 13)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [A Theory of the Distortion-Perception Tradeoff in Wasserstein Space](https://mlsanity.com/paper/2107.02555/) (2021)
- [DeepPET: A deep encoder-decoder network for directly solving the PET reconstruction inverse problem](https://mlsanity.com/paper/1804.07851/) (2018)
- [Posterior-Mean Rectified Flow: Towards Minimum MSE Photo-Realistic Image Restoration](https://mlsanity.com/paper/2410.00418/) (2024)
- [TransEM:Residual Swin-Transformer based regularized PET image reconstruction](https://mlsanity.com/paper/2205.04204/) (2022)
- [DirectPET: Full Size Neural Network PET Reconstruction from Sinogram Data](https://mlsanity.com/paper/1908.07516/) (2019)
- [LegoPET: Hierarchical Feature Guided Conditional Diffusion for PET Image Reconstruction](https://mlsanity.com/paper/2411.16629/) (2024)

## Abstract (arXiv)

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.