  In the past years modern mathematical methods for image analysis have led to
a revolution in many fields, from computer vision to scientific imaging.
However, some recently developed image processing techniques successfully
exploited by other sectors have been rarely, if ever, experimented on
astronomical observations. We present here tests of two classes of variational
image enhancement techniques: "structure-texture decomposition" and
"super-resolution" showing that they are effective in improving the quality of
observations. Structure-texture decomposition allows to recover faint sources
previously hidden by the background noise, effectively increasing the depth of
available observations. Super-resolution yields an higher-resolution and a
better sampled image out of a set of low resolution frames, thus mitigating
problematics in data analysis arising from the difference in
resolution/sampling between different instruments, as in the case of EUCLID VIS
and NIR imagers.
