Estimation of instrument and noise parameters for inverse problem based on prior diffusion model
This work addresses a thorny issue in inverse problems for researchers in computational statistics, offering incremental improvements in parameter estimation and uncertainty quantification.
The paper tackles the estimation of observation parameters in inverse problems with Bayesian regularization and diffusion priors, proposing a strategy that enables optimal estimation of both parameters and the image of interest, with numerical experiments confirming computational efficiency and quality.
This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems. The focus is on cases where regularization is introduced in a Bayesian framework and the prior is modeled by a diffusion process. In this context, the issue of posterior sampling is well known to be thorny, and a recent paper proposes a notably simple and effective solution. Consequently, it offers an remarkable additional flexibility when it comes to estimating observation parameters. The proposed strategy enables us to define an optimal estimator for both the observation parameters and the image of interest. Furthermore, the strategy provides a means of quantifying uncertainty. In addition, MCMC algorithms allow for the efficient computation of estimates and properties of posteriors, while offering some guarantees. The paper presents several numerical experiments that clearly confirm the computational efficiency and the quality of both estimates and uncertainties quantification.