Super-resolution in map-making based on a physical instrument model and regularized inversion

Application to SPIRE/Herschel

¹ Laboratoire des Signaux et Systèmes (cnrs – Supélec – Univ. Paris-Sud 11), Plateau de Moulon, 91192 Gif-sur-Yvette, France
e-mail: orieux@lss.supelec.fr; rodet@lss.supelec.fr
² Univ. Bordeaux, IMS, UMR 5218, 33400 Talence, France
e-mail: Giova@IMS-Bordeaux.fr
³ Institut d’Astrophysique Spatiale (cnrs – Univ. Paris-Sud 11), 91 405 Orsay, France
e-mail: abergel@ias.u-psud.fr

Received: 3 March 2011
Accepted: 5 December 2011

Abstract

We investigate super-resolution methods for image reconstruction from data provided by a family of scanning instruments like the Herschel observatory. To do this, we constructed a model of the instrument that faithfully reflects the physical reality, accurately taking the acquisition process into account to explain the data in a reliable manner. The inversion, i.e. the image reconstruction process, is based on a linear approach resulting from a quadratic regularized criterion and numerical optimization tools. The application concerns the reconstruction of maps for the SPIRE instrument of the Herschel observatory. The numerical evaluation uses simulated and real data to compare the standard tool (coaddition) and the proposed method. The inversion approach is capable to restore spatial frequencies over a bandwidth four times that possible with coaddition and thus to correctly show details invisible on standard maps. The approach is also applied to real data with significant improvement in spatial resolution.