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 information. DeepRED is a typical representation learning that combines deep image prior (DIP) and regularization by denoising (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.