Unsupervised PET Reconstruction from a Bayesian Perspective

TL;DR

This paper introduces an unsupervised PET image reconstruction method using a Bayesian approach that leverages DeepRED and a DnCNN-like denoiser, improving image quality without requiring labeled data.

Contribution

It presents a novel Bayesian framework for PET reconstruction that combines DeepRED with a DnCNN-like denoiser and Gaussian noise injection, enhancing regularization and reconstruction quality.

Findings

Outperforms classic and state-of-the-art methods in qualitative assessments

Achieves higher quantitative accuracy in PET image reconstruction

Demonstrates robustness on brain and whole-body datasets

Abstract

Positron emission tomography (PET) reconstruction has become an ill-posed inverse problem due to low-count projection data, and a robust algorithm is urgently required to improve imaging quality. Recently, the deep image prior (DIP) has drawn much attention and has been successfully applied in several image restoration tasks, such as denoising and inpainting, since it does not need any labels (reference image). However, overfitting is a vital defect of this framework. Hence, many methods have been proposed to mitigate this problem, and DeepRED is a typical representation that combines DIP and regularization by denoising (RED). In this article, we leverage DeepRED from a Bayesian perspective to reconstruct PET images from a single corrupted sinogram without any supervised or auxiliary information. In contrast to the conventional denoisers customarily used in RED, a DnCNN-like denoiser, which can add an adaptive constraint to DIP and facilitate the computation of derivation, is employed. Moreover, to further enhance the regularization, Gaussian noise is injected into the gradient updates, deriving a Markov chain Monte Carlo (MCMC) sampler. Experimental studies on brain and whole-body datasets demonstrate that our proposed method can achieve better performance in terms of qualitative and quantitative results compared to several classic and state-of-the-art methods.