Regularization of inverse problems is of paramount importance in computational imaging. The ability of neural networks to learn efficient image representations has been recently exploited to design powerful data-driven regularizers. While state-of-the-art plug-and-play methods rely on an implicit regularization provided by neural denoisers, alternative Bayesian approaches consider Maximum A Posteriori (MAP) estimation in the latent space of a generative model, thus with an explicit regularization. However, state-of-the-art deep generative models require a huge amount of training data compared to denoisers. Besides, their complexity hampers the optimization involved in latent MAP derivation. In this work, we first propose to use compressive autoencoders instead. These networks, which can be seen as variational autoencoders with a flexible latent prior, are smaller and easier to train than state-of-the-art generative models. As a second contribution, we introduce the Variational Bayes Latent Estimation (VBLE) algorithm, which performs latent estimation within the framework of variational inference. Thanks to a simple yet efficient parameterization of the variational posterior, VBLE allows for fast and easy (approximate) posterior sampling. Experimental results on image datasets BSD and FFHQ demonstrate that VBLE reaches similar performance than state-of-the-art plug-and-play methods, while being able to quantify uncertainties faster than other existing posterior sampling techniques.

翻译：在计算成像中，逆问题的正则化至关重要。神经网络学习高效图像表示的能力近期被用于设计强大的数据驱动正则化器。当前最先进的即插即用方法依赖于神经降噪器提供的隐式正则化，而另一种贝叶斯方法则在生成模型的潜空间中考虑最大后验估计，从而实现了显式正则化。然而，与降噪器相比，最先进的深度生成模型需要大量训练数据，且其复杂性阻碍了潜空间最大后验估计推导中的优化过程。本文首先提出使用压缩自编码器替代上述方案。这类网络可视为带有灵活潜先验的变分自编码器，其规模更小且比最先进的生成模型更易训练。作为第二项贡献，我们引入了变分贝叶斯潜估计（VBLE）算法，该算法在变分推断框架内进行潜估计。得益于变分后验的简洁高效参数化，VBLE可实现快速易行的近似后验采样。在BSD和FFHQ图像数据集上的实验结果表明，VBLE在达到与最先进即插即用方法相当性能的同时，其不确定性量化速度优于其他现有后验采样技术。