Estimating hyperparameters and instrument parameters in regularized inversion. Illustration for SPIRE/Herschel map making

TL;DR

This paper presents a Bayesian approach using MCMC sampling for estimating hyperparameters and instrument parameters in regularized image reconstruction, demonstrated on Herschel SPIRE data, enhancing astrophysical imaging accuracy.

Contribution

Introduces a Bayesian framework with MCMC sampling for unsupervised hyperparameter and instrument parameter estimation in regularized inversion.

Findings

Hyperparameters and instrument parameters are accurately estimated.

Method is validated on simulated and real Herschel SPIRE data.

Enhances imaging quality in astrophysics applications.

Abstract

We describe regularized methods for image reconstruction and focus on the question of hyperparameter and instrument parameter estimation, i.e. unsupervised and myopic problems. We developed a Bayesian framework that is based on the \post density for all unknown quantities, given the observations. This density is explored by a Markov Chain Monte-Carlo sampling technique based on a Gibbs loop and including a Metropolis-Hastings step. The numerical evaluation relies on the SPIRE instrument of the Herschel observatory. Using simulated and real observations, we show that the hyperparameters and instrument parameters are correctly estimated, which opens up many perspectives for imaging in astrophysics.