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.

翻译：本文提出利用深度层级变分自编码器（HVAE）作为图像先验，对不适定反问题进行正则化。所提方法综合了以下两方面的优势：i) 基于去噪器的即插即用方法，以及 ii) 基于生成模型的反问题求解方法。首先，我们利用VAE的特性设计了一种高效算法，该算法继承了即插即用（PnP）方法的收敛性保证。其次，我们的方法不局限于特定数据集，所提出的PnP-HVAE模型能够求解任意尺寸自然图像的图像复原问题。实验表明，所提出的PnP-HVAE方法在性能上与基于去噪器的SOTA PnP方法以及其他基于生成模型的SOTA复原方法相当。