Self-supervised Deep Image Restoration via Adaptive Stochastic Gradient Langevin Dynamics

While supervised deep learning has been a prominent tool for solving many image restoration problems, there is an increasing interest on studying self-supervised or un-supervised methods to address the challenges and costs of collecting truth images. Based on the neuralization of a Bayesian estimator of the problem, this paper presents a self-supervised deep learning approach to general image restoration problems. The key ingredient of the neuralized estimator is an adaptive stochastic gradient Langevin dy-namics algorithm for efficiently sampling the posterior distri-bution of network weights. The proposed method is applied on two image restoration problems: compressed sensing and phase retrieval. The experiments on these applications showed that the proposed method not only outperformed existing non-learning and unsupervised solutions in terms of image restoration quality, but also is more computationally efficient.