Unsupervised PET Reconstruction from a Bayesian Perspective

Positron emission tomography (PET) reconstruction becomes an ill-posed inverse problem due to the low-count projection data (sinogram). In this paper, we leverage DeepRED from a Bayesian perspective to reconstruct PET image from a single corrupted sinogram without any supervised or auxiliary in-formation. DeepRED is a typical representation learning that combines deep image prior (DIP) and regularization by de-noising (RED) to mitigate the overfitting of network training. Instead of the conventional denoisers usually used in RED, DnCNN-like denoiser, which can constrain the DIP adaptively and facilitate the derivation, is employed. Moreover, stochastic gradient Langevin dynamics (SGLD) is utilized to approximate the Markov chain Monte Carlo (MCMC) sampler. Specifically, Gaussian noise is injected into the gradient updates to further relieve the overfitting. Experimental studies on whole-body dataset demonstrate that our proposed method can achieve better performance compared to several classic and state-of-the-art methods in both qualitative and quantitative aspects.

1. INTRODUCTION

Positron emission tomography (PET) can reflect the molecular level activities of various organs and tissues in vivo by virtue of injecting specific radioactive tracers. Since the amount of injected radiotracer in current protocols may in-crease the potential risks of radiation exposure for human body, how to reduce the dose while maintaining the imaging quality is of great clinical significance. However, simply reducing the injected dose can result in low-count PET projection data (sinogram), which leads to undesired noise and artifacts in the reconstructed images, thus negatively affecting the subsequent clinical diagnosis.