论文标题
使用深层生成先验的非线性成像模型的贝叶斯反演
Bayesian Inversion for Nonlinear Imaging Models using Deep Generative Priors
论文作者
论文摘要
大多数现代成像系统都结合了一条计算管道，从获得的测量中推断了感兴趣的图像。解决此类逆向问题的贝叶斯方法涉及图像后验分布的表征。这取决于成像系统的模型以及有关感兴趣形象的先验知识。在这项工作中，我们为非线性成像模型提供了一个贝叶斯重建框架，我们通过深层生成模型指定图像上的先验知识。我们基于大都市调整后的Langevin算法开发一种可拖动的后验采样方案，用于非线性逆问题类别，在这些非线性逆问题中，正向模型具有类似神经网络的结构。该课程包括最实用的成像方式。我们介绍了增强的深层生成先验的概念，以适当地处理定量图像的恢复。我们通过将其应用于两个非线性成像阶相检索和光学衍射断层扫描来说明我们框架的优势。
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.
