Improving resolution and depth of astronomical observations via modern mathematical methods for image analysis

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.