  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, ie 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.
