Sampling Strategies in Bayesian Inversion: A Study of RTO and Langevin Methods

TL;DR

This paper compares RTO and Langevin sampling methods for inverse problems, analyzing their theoretical differences and practical performance in imaging tasks like deblurring and inpainting.

Contribution

It provides a detailed comparison of RTO and Langevin methods, highlighting their conceptual differences and practical robustness in inverse imaging problems.

Findings

RTO is more robust to parameter choices.

Sampling method impacts reconstruction quality.

Theoretical differences influence practical performance.

Abstract

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.