Estimation of instrument and noise parameters for inverse problem based on prior diffusion model

TL;DR

This paper introduces a Bayesian diffusion prior-based method for estimating observation and noise parameters in inverse problems, enhancing parameter estimation and uncertainty quantification with efficient MCMC algorithms.

Contribution

It proposes a novel strategy for joint estimation of observation parameters and images within a diffusion prior Bayesian framework, improving flexibility and computational efficiency.

Findings

The method accurately estimates observation and noise parameters.

Numerical experiments confirm computational efficiency and high-quality uncertainty quantification.

The approach outperforms existing methods in inverse problem parameter estimation.

Abstract

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.