# Estimating Uncertainty in PET Image Reconstruction via Deep Posterior Sampling

arXiv: https://arxiv.org/abs/2306.04664 · HTML: https://mlsanity.com/paper/2306.04664/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 53 references that are in the map.
- First posted on arXiv 7 Jun 2023.

## Builds on (most cited first, 25 of 25)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [Real-ESRGAN: Training Real-World Blind Super-Resolution with Pure Synthetic Data](https://mlsanity.com/paper/2107.10833/) (2021)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Which Training Methods for GANs do actually Converge?](https://mlsanity.com/paper/1801.04406/) (2018)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Mode Seeking Generative Adversarial Networks for Diverse Image Synthesis](https://mlsanity.com/paper/1903.05628/) (2019)
- [Diversity-Sensitive Conditional Generative Adversarial Networks](https://mlsanity.com/paper/1901.09024/) (2019)
- [Deep Bayesian Inversion](https://mlsanity.com/paper/1811.05910/) (2018)
- [Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems](https://mlsanity.com/paper/2211.12343/) (2022)
- [DeepPET: A deep encoder-decoder network for directly solving the PET reconstruction inverse problem](https://mlsanity.com/paper/1804.07851/) (2018)
- [High Perceptual Quality Image Denoising with a Posterior Sampling CGAN](https://mlsanity.com/paper/2103.04192/) (2021)
- [Towards Lower-Dose PET using Physics-Based Uncertainty-Aware Multimodal Learning with Robustness to Out-of-Distribution Data](https://mlsanity.com/paper/2107.09892/) (2021)
- [Conditional Injective Flows for Bayesian Imaging](https://mlsanity.com/paper/2204.07664/) (2022)
- [Full-count PET Recovery from Low-count Image Using a Dilated Convolutional Neural Network](https://mlsanity.com/paper/1910.11865/) (2019)
- [Implicit Neural Representation for Mesh-Free Inverse Obstacle Scattering](https://mlsanity.com/paper/2206.02027/) (2022)
- [High-Perceptual Quality JPEG Decoding via Posterior Sampling](https://mlsanity.com/paper/2211.11827/) (2022)
- [Super-resolution PET imaging using convolutional neural networks](https://mlsanity.com/paper/1906.03645/) (2019)

## Built on by (most cited first, 2 of 2)

- [A review of uncertainty quantification in medical image analysis: probabilistic and non-probabilistic methods](https://mlsanity.com/paper/2310.06873/) (2023)
- [Comparison of Deterministic and Probabilistic Machine Learning Algorithms for Precise Dimensional Control and Uncertainty Quantification in Additive Manufacturing](https://mlsanity.com/paper/2509.16233/) (2025)

## Abstract (arXiv)

Positron emission tomography (PET) is an important functional medical imaging technique often used in the evaluation of certain brain disorders, whose reconstruction problem is ill-posed. The vast majority of reconstruction methods in PET imaging, both iterative and deep learning, return a single estimate without quantifying the associated uncertainty. Due to ill-posedness and noise, a single solution can be misleading or inaccurate. Thus, providing a measure of uncertainty in PET image reconstruction can help medical practitioners in making critical decisions. This paper proposes a deep learning-based method for uncertainty quantification in PET image reconstruction via posterior sampling. The method is based on training a conditional generative adversarial network whose generator approximates sampling from the posterior in Bayesian inversion. The generator is conditioned on reconstruction from a low-dose PET scan obtained by a conventional reconstruction method and a high-quality magnetic resonance image and learned to estimate a corresponding standard-dose PET scan reconstruction. We show that the proposed model generates high-quality posterior samples and yields physically-meaningful uncertainty estimates.