In this paper, we propose to regularize ill-posed inverse problems using a deep hierarchical variational autoencoder (HVAE) as an image prior. The proposed method synthesizes the advantages of i) denoiser-based Plug \& Play approaches and ii) generative model based approaches to inverse problems. First, we exploit VAE properties to design an efficient algorithm that benefits from convergence guarantees of Plug-and-Play (PnP) methods. Second, our approach is not restricted to specialized datasets and the proposed PnP-HVAE model is able to solve image restoration problems on natural images of any size. Our experiments show that the proposed PnP-HVAE method is competitive with both SOTA denoiser-based PnP approaches, and other SOTA restoration methods based on generative models.
@article{arxiv.2303.11217,
title = {Inverse problem regularization with hierarchical variational autoencoders},
author = {Jean Prost and Antoine Houdard and Andrés Almansa and Nicolas Papadakis},
journal= {arXiv preprint arXiv:2303.11217},
year = {2024}
}