Adversarial EM for variational deep learning: Application to semi-supervised image quality enhancement in low-dose PET and low-dose CT.

In positron emission tomography (PET) and X-ray computed tomography (CT), reducing radiation dose can cause significant degradation in image quality. For image quality enhancement in low-dose PET and CT, we propose a novel theoretical adversarial and variational deep neural network (DNN) framework relying on expectation maximization (EM) based learning, termed adversarial EM (AdvEM). AdvEM proposes an encoder-decoder architecture with a multiscale latent space, and generalized-Gaussian models enabling datum-specific robust statistical modeling in latent space and image space. The model robustness is further enhanced by including adversarial learning in the training protocol. Unlike typical variational-DNN learning, AdvEM proposes latent-space sampling from the posterior distribution, and uses a Metropolis-Hastings scheme. Unlike existing schemes for PET or CT image enhancement which train using pairs of low-dose images with their corresponding normal-dose versions, we propose a semi-supervised AdvEM (ssAdvEM) framework that enables learning using a small number of normal-dose images. AdvEM and ssAdvEM enable per-pixel uncertainty estimates for their outputs. Empirical analyses on real-world PET and CT data involving many baselines, out-of-distribution data, and ablation studies show the benefits of the proposed framework.