  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.
