Most modern imaging systems incorporate a computational pipeline to infer the image of interest from acquired measurements. The Bayesian approach to solve such ill-posed inverse problems involves the characterization of the posterior distribution of the image. It depends on the model of the imaging system and on prior knowledge on the image of interest. In this work, we present a Bayesian reconstruction framework for nonlinear imaging models where we specify the prior knowledge on the image through a deep generative model. We develop a tractable posterior-sampling scheme based on the Metropolis-adjusted Langevin algorithm for the class of nonlinear inverse problems where the forward model has a neural-network-like structure. This class includes most practical imaging modalities. We introduce the notion of augmented deep generative priors in order to suitably handle the recovery of quantitative images.We illustrate the advantages of our framework by applying it to two nonlinear imaging modalities-phase retrieval and optical diffraction tomography.

翻译：大多数现代成像系统都包含一个计算流程，用于从采集的测量值中推断出感兴趣的图像。解决此类病态逆问题的贝叶斯方法涉及图像后验分布的表征。该分布取决于成像系统的模型以及关于感兴趣图像的先验知识。在本工作中，我们提出了一种针对非线性成像模型的贝叶斯重建框架，其中通过深度生成模型来指定图像的先验知识。对于前向模型具有类神经网络结构的一类非线性逆问题，我们开发了一种基于Metropolis调整Langevin算法的易处理后验采样方案。此类问题涵盖大多数实际成像模态。我们引入了增广深度生成先验的概念，以恰当处理定量图像的恢复问题。通过将我们的框架应用于两种非线性成像模态——相位恢复和光学衍射断层成像，我们展示了其优势。