Modeling statistics of image priors is useful for image super-resolution, but little attention has been paid from the massive works of deep learning-based methods. In this work, we propose a Bayesian image restoration framework, where natural image statistics are modeled with the combination of smoothness and sparsity priors. Concretely, firstly we consider an ideal image as the sum of a smoothness component and a sparsity residual, and model real image degradation including blurring, downscaling, and noise corruption. Then, we develop a variational Bayesian approach to infer their posteriors. Finally, we implement the variational approach for single image super-resolution (SISR) using deep neural networks, and propose an unsupervised training strategy. The experiments on three image restoration tasks, \textit{i.e.,} ideal SISR, realistic SISR, and real-world SISR, demonstrate that our method has superior model generalizability against varying noise levels and degradation kernels and is effective in unsupervised SISR. The code and resulting models are released via \url{https://zmiclab.github.io/projects.html}.
@article{arxiv.2204.00623,
title = {Bayesian Image Super-Resolution with Deep Modeling of Image Statistics},
author = {Shangqi Gao and Xiahai Zhuang},
journal= {arXiv preprint arXiv:2204.00623},
year = {2022}
}