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

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 posterior 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. 1. Unsupervised myopic inversion The agreement of physical models and observations is a crucial question in astrophysics, however , observation instruments inevitably have defects and limitations (limited pass-band, non-zero response time, attenuation, error and uncertainty, etc.). Their inversion by numerical processing must, as far as possible, be based on an instrument model that includes a description of