Super-resolution in map-making based on a physical instrument model and regularized inversion. Application to SPIRE/Herschel

This article concerns over-resolution methods for image reconstruction from data provided by a family of scanning instruments like the Herschel observatory. The work is centered on building a model of the instrument that faithfully reflects the physical reality, accurately taking the acquisition process into account so as 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 inversion process produces maps that are over-resolved with respect to the nominal resolution of the instrument. 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. We demonstrate a capacity to restore spatial frequencies over a bandwidth four times that possible with coaddition and thus to correctly show details invisible on standard maps. The proposed approach is also applied to real data with significant improvement in spatial resolution.