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 of the latent MAP. In this work, we propose to use compressive autoencoders for latent estimation. 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. We then introduce the Variational Bayes Latent Estimation (VBLE) algorithm, which performs this estimation within the framework of variational inference. This 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：逆问题的正则化在计算成像中至关重要。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。虽然最先进的即插即用方法依赖于神经网络去噪器提供的隐式正则化，但替代的贝叶斯方法在生成模型的潜在空间中考虑最大后验概率估计，从而提供显式正则化。然而，与去噪器相比，最先进的深度生成模型需要大量训练数据。此外，其复杂性阻碍了潜在最大后验概率的优化。在本文中，我们提出使用压缩自编码器进行潜在估计。这些网络可视为具有灵活潜在先验的变分自编码器，相较于最先进的生成模型体积更小且更易训练。随后我们引入变分贝叶斯潜在估计算法，该算法在变分推理框架内执行估计，实现快速且简便的（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，能比其他现有后验采样技术更快地量化不确定性。