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

¹ Institut d’Astrophysique de Paris (CNRS – Univ. Paris 6), 75014 Paris, France
e-mail: orieux@iap.fr
² Univ. Bordeaux, IMS, UMR 5218, 33400 Talence, France
e-mail: Giova@IMS-Bordeaux.fr
³ Laboratoire des Signaux et Systèmes (CNRS – Supélec – Univ. Paris-Sud 11), 91192 Gif-sur-Yvette, France
e-mail: orieux,rodet@lss.supelec.fr
⁴ Institut d’Astrophysique Spatiale (CNRS – Univ. Paris-Sud 11), 91405 Orsay, France
e-mail: abergel@ias.u-psud.fr

Received: 5 July 2012
Accepted: 19 October 2012

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 posteriordensity 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.