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PET image denoising based on denoising diffusion probabilistic models
Kuang Gong, Keith A. Johnson, Georges El Fakhri, Quanzheng Li, Tinsu Pan
TL;DR
Limited counts and physical degradation reduce PET image quality. This work evaluates DDPM-based denoising strategies using PET and MR information across two tracer datasets. PET-informed DDPMs outperform nonlocal mean and Unet methods, while MR input with PET data consistency achieves the strongest regional and surface results.
Problem
Limited counts and physical degradation reduce PET image quality, motivating improved denoising methods.
Method
The study evaluates DDPM-based PET denoising strategies that embed PET and MR information in network inputs or inference-time data consistency.
Results
DDPM frameworks including PET information perform better than nonlocal mean and Unet-based denoising methods.
Takeaways & Limitations
Using MR prior as network input with PET embedded as an inference-time data-consistency constraint achieves the best regional and surface performance.
Takeaways & Limitations
Relying only on MR prior can produce large bias because PET uptake has a high dynamic range across regions.
Abstract
from arXiv · showhide
Due to various physical degradation factors and limited counts received, PET image quality needs further improvements. The denoising diffusion probabilistic models (DDPM) are distribution learning-based models, which try to transform a normal distribution into a specific data distribution based on iterative refinements. In this work, we proposed and evaluated different DDPM-based methods for PET image denoising. Under the DDPM framework, one way to perform PET image denoising is to provide the PET image and/or the prior image as the network input. Another way is to supply the prior image as the input with the PET image included in the refinement steps, which can fit for scenarios of different noise levels. 120 18F-FDG datasets and 140 18F-MK-6240 datasets were utilized to evaluate the proposed DDPM-based methods. Quantification show that the DDPM-based frameworks with PET information included can generate better results than the nonlocal mean and Unet-based denoising methods. Adding additional MR prior in the model can help achieve better performance and further reduce the uncertainty during image denoising. Solely relying on MR prior while ignoring the PET information can result in large bias. Regional and surface quantification shows that employing MR prior as the network input while embedding PET image as a data-consistency constraint during inference can achieve the best performance. In summary, DDPM-based PET image denoising is a flexible framework, which can efficiently utilize prior information and achieve better performance than the nonlocal mean and Unet-based denoising methods.
Abstract
The paper addresses PET image denoising using diffusion models and low-dose PET imaging.
- The study concerns PET image denoising, denoising diffusion probabilistic models, low-dose PET, and generative models.
Introduction
PET image quality is limited by degradation factors and low counts, motivating denoising methods that preserve detail across variable noise levels. The paper evaluates DDPMs that incorporate PET and anatomical prior information.
- Limited PET counts reduce signal-to-noise ratio and resolution, challenging high-quality imaging.
- CNN-based denoising can produce over-smoothed outputs and may be compromised by training–testing data-distribution mismatch.
- DDPMs transform a normal distribution toward a target data distribution through iterative noise-removal refinements.
- PET has complex uptake and noise distributions, while corresponding CT or MR scans provide available anatomical prior information.
- The study explores embedding PET and MR information in DDPMs and compares them with nonlocal mean and Unet denoising.
- Evaluation uses 120 18F-FDG datasets and 140 18F-MK-6240 datasets with global and regional quantitative metrics.
Materials and methods
The methods formulate PET denoising as conditional DDPM sampling and evaluate alternative uses of PET and MR information across two tracer datasets.
- DDPM model: DDPM sampling approximates an intractable reverse transition by repeatedly refining noisy samples toward the target data distribution.
- Conditional PET image denoising based on DDPM: A conditional framework can provide noisy PET and prior images as score-function inputs, but requires specific low- and high-quality training pairs.
- Conditional PET image denoising based on DDPM: Alternatively, the prior image is supplied to the score function while noisy PET enters inference, supporting varied noise levels without paired training data.
- Datasets: The experiments use 120 18F-FDG datasets and 140 18F-MK-6240 datasets, with low-dose images formed from one-quarter event data.
- Data analysis: Methods are assessed using PSNR, SSIM, Wilcoxon signed-rank tests, cortical-region analysis, and PET relative-error surface maps.
Results
DDPM methods that retain PET information outperform reference denoising approaches, while MR prior and PET data consistency improve image quality, regional accuracy, and uncertainty.
- 18F-FDG results: DDPM-PET achieves better quantification results than the nonlocal mean and Unet reference methods on 30 test datasets.
- 18F-MK-6240 results: DDPM-PETMR provides higher image resolution than DDPM-PET, demonstrating benefit from adding MR prior as network input.
- 18F-MK-6240 results: DDPM-MR-PETCon produces results more similar to normal-dose images and higher image contrast than Unet.
- Quantitative results: Global quantification ranks DDPM-PETMR first and DDPM-MR-PETCon second, whereas regional and surface analyses rank DDPM-MR-PETCon first.
- Quantitative results: DDPM-MR-PETCon supports different noise levels and is more flexible than DDPM-PETMR.
- Uncertainty analysis: Adding MR prior reduces uncertainty, and embedding PET during refinement reduces it further compared with supplying PET only as network input.
Discussion
The evaluated DDPM framework benefits from incorporating PET information and MR priors, with PET-constrained inference offering a favorable balance of performance, noise-level flexibility, and reconstruction potential. The study also identifies computational and dataset-scope limitations, including slow 3D inference and evaluation restricted to brain PET.
- DDPM frameworks including PET information achieved better performance than NLM and Unet-based denoising methods.
- Diffusion models can generate uncertainty maps from multiple realizations, with potential use in progression tracking and longitudinal studies.
- Adding MR prior images as network inputs improved global and regional performance and reduced uncertainty.
- Relying only on MR priors can produce large bias because PET uptake varies across regions.
- PET-constrained inference improved DDPM-MR results, while DDPM-MR-PETCon performed better locally and supported different PET noise levels.
- DDPM-MR-PETCon was preferred over DDPM-PETMR for performance, noise-level invariability, and potential extension to PET reconstruction.
- The methods used 2D networks because 3D training was four times slower, while inference took around 50 minutes for one 3D dataset.
- Future work includes efficient 3D training, shorter inference, and evaluation on whole-body PET datasets with different tracers.
Conclusion
The study developed and evaluated DDPM-based PET denoising frameworks on 18F-FDG and 18F-MK-6240 datasets. Frameworks incorporating PET information outperformed nonlocal mean and Unet methods, while MR priors improved performance and reduced uncertainty.
- DDPM-based PET denoising frameworks were developed and evaluated using 18F-FDG and 18F-MK-6240 datasets.
- Frameworks including PET information achieved better performance than nonlocal mean and Unet-based denoising methods.
- Adding an MR prior improved denoising performance and further reduced uncertainty during image denoising.
- Future work will extend the framework to 3D networks, reduce inference time, and evaluate whole-body PET datasets using different tracers.
Declarations
The declarations report funding, competing interests, ethics compliance, and consent procedures, alongside figures documenting datasets, methods, quantitative metrics, regional analyses, surface errors, and uncertainty maps.
- The work was supported by NIH grants R21AG067422, R03EB030280, P41EB022544, P01AG036694, and R01AG078250.
- The authors reported no relevant financial or non-financial competing interests.
- Human-participant procedures followed institutional or national ethical standards and the 1964 Helsinki Declaration; consent was waived for retrospective 18F-FDG data and obtained for 18F-MK-6240 data.
- Figures document DDPM processing, PET views, PSNR and SSIM comparisons, cortical-region and surface analyses, and uncertainty maps across different methods.