Deep Unfolding With Normalizing Flow Priors for Inverse Problems

Xinyi Wei, Hans Van Gorp, Lizeth Gonzalez-Carabarin, Daniel Freedman, Yonina C. Eldar, Ruud J. G. van Sloun

Abstract: Many application domains, spanning from computational photography to medical imaging, require recovery of high-fidelity images from noisy, incomplete or partial/compressed measurements. State-of-the-art methods for solving these inverse problems combine deep learning with iterative model-based solvers, a concept known as deep algorithm unfolding or unrolling. By combining a-priori knowledge of the forward measurement model with learned proximal image-to-image mappings based on deep networks, these methods yield solutions that are both physically feasible (data-consistent) and perceptually plausible (consistent with prior belief). However, current proximal mappings based on (predominantly convolutional) neural networks only implicitly learn such image priors. In this paper, we propose to make these image priors fully explicit by embedding deep generative models in the form of normalizing flows within the unfolded proximal gradient algorithm, and training the entire algorithm end-to-end for a given task. We demonstrate that the proposed method outperforms competitive baselines on various image recovery tasks, spanning from image denoising to inpainting and deblurring, effectively adapting the prior to the restoration task at hand.