END-TO-END PET IMAGE RECONSTRUCTION VIA A POSTERIOR-MEAN DIFFUSION - Model - Yiran Sun⋆, Osama Mawlawi

Oct 17, 2026

Positron Emission Tomography (PET) is a functional imaging modality that visualizes biochemical and physiological processes across tissues. Recent deep learning approaches can map sinograms directly to PET images, but regression models produce overly smoothed results, while GAN and posterior sampling methods may introduce artifacts. PMDM-PET proposes a posterior-mean denoising diffusion framework to optimize the perception–distortion tradeoff by transporting posterior-mean predictions to ground-truth distributions, improving PSNR/SSIM/NRMSE. Experiments show superior performance over five SOTA baselines in both visual quality and quantitative metrics.

LanguageEnglish

CategoryResearch & Report

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Abstract

1. Introduction

PET reconstruction background and methods

Limitations of DL approaches and motivation

END-TO-END PET IMAGE RECONSTRUCTION VIA A POSTERIOR-MEAN DIFFUSION MODEL Yiran Sun⋆,†, Osama Mawlawi†,⋆ ⋆ Department of Electrical and Computer Engineering, Rice University, Houston, USA † Department of Imaging Physics, University of Texas MD Anderson Cancer Center, Houston, USA arXiv :2503 .08546v2 [ ee ss .IV] 15 Jan 2026 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. Index Terms— Deep Learning, Image Reconstruction, PET 1. INTRODUCTION Positron Emission Tomography (PET) is a functional imaging modality that visualizes biochemical and physiological processes across tissues. During acquisition, high-energy photons from positron annihilation are detected by ringstructured arrays within a PET scanner. Photon counts from multiple angles are compiled into projections and arranged into sinograms, forming the basis for PET image reconstruction [1] . Over the past few decades, various approaches have been developed to reconstruct high-quality PET im- ages from sinograms, broadly categorized into four main directions: 1) Traditional analytical methods, such as filtered back-projection (FBP); 2) Iterative techniques, including ordered subsets expectation maximization (OSEM), maximumlikelihood expectation maximization (MLEM) [2], and penalized log-likelihood (PLL) methods [3]; 3) Deep learningbased approaches [4, 5, 6, 7, 8]; 4) Compressed sensing-based methods [9] . Some of these methods have several limitations, for example, traditional analytical approaches are highly sensitive to noise and prone to streak artifacts, iterative methods often suffer from high computational complexity, and compressed sensing techniques rely heavily on the choice of sparsifying transforms and regularization terms. In this study, we focus on supervised deep learning (DL) methods that directly map sinograms to PET images, as they effectively model complex nonlinear relationships without being constrained by external physical factors. However, regression-based DL approaches trained with mean square error (MSE) often produce overly smooth textures and suboptimal perceptual quality (i.e., low distortion, low perceptual quality) [10] . To improve the perceptual quality in reconstructed images, conditional generative models (cGMs) have emerged as a promising posterior sampling approach, which incorporates novel loss terms to capture underlying posterior distributions and generate realistic images from corresponding measurements. However, cGMs present significant challenges: generative adversarial net

FAQs

What problem does PMDM-PET address in PET image reconstruction?

PMDM-PET targets the perception–distortion tradeoff: regression methods can over-smooth reconstructions, while generative and posterior sampling methods may introduce artifacts, limiting clinical applicability.

How does PMDM-PET generate PET images from sinograms?

It first computes posterior-mean PET predictions under MSE, then uses a conditional diffusion probabilistic model to optimally transport these predictions toward the ground-truth PET distribution using perception supervision.

What metrics are used to evaluate PMDM-PET?

PMDM-PET is evaluated with qualitative visual inspection and quantitative pixel-wise metrics including PSNR, SSIM, and NRMSE.

Oct 17, 2026

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