This paper studies two classes of sampling methods for the solution of inverse problems, namely Randomize-Then-Optimize (RTO), which is rooted in sensitivity analysis, and Langevin methods, which are rooted in the Bayesian framework. The two classes of methods correspond to different assumptions and yield samples from different target distributions. We highlight the main conceptual and theoretical differences between the two approaches and compare them from a practical point of view by tackling two classical inverse problems in imaging: deblurring and inpainting. We show that the choice of the sampling method has a significant impact on the quality of the reconstruction and that the RTO method is more robust to the choice of the parameters.

本文研究两类求解逆问题的抽样方法，即基于敏感性分析的随机优化（RTO）和基于贝叶斯框架的朗格温方法。这两类方法对应于不同的假设，并从不同的目标分布中获得样本。我们强调了两种方法之间的主要概念和理论差异，并从实际角度通过处理图像的两个经典逆问题（去模糊和修复）进行了比较。我们展示了抽样方法的选择对重建质量的显著影响，而RTO方法对参数选择更加健壮。

贝叶斯反演中的抽样策略：RTO和Langevin方法的研究