Uncertainty-Informed Bayesian PET Image Reconstruction Using a Deep Image Prior

Model-based image reconstruction (MBIR) methods using convolutional neural networks (CNNs) as priors have demonstrated superior image quality and robustness compared to conventional methods. Studies have explored MBIR combined with supervised and unsupervised denoising techniques for image reconstruction in magnetic resonance imaging (MRI) and positron emission tomography (PET). Unsupervised methods like the deep image prior (DIP) have shown promising results and are less prone to hallucinations. However, since the noisy image is used as a reference, strategies to prevent overfitting are unclear. Recently, Bayesian DIP (BDIP) networks that model uncertainty tend to prevent overfitting without requiring early stopping. However, BDIP has not been studied with data-fidelity term for image reconstruction. In this work, we propose an MBIR framework with a modified BDIP. Specifically, a novel uncertainty-based penalty is included to the BDIP to improve reconstruction across iterations. Results on simulated and in vivo data show that our method yields improved reconstruction compared to methods with conventional priors and typical DIP without uncertainty. Notably, the uncertainty maps across iterations provide insights on improving image quality and can aid in risk management.