  Kernel-phase is a recently developed paradigm that tackles the classical
problem of image deconvolution, based on an interferometric point of view of
image formation. Kernel-phase inherits and borrows from the notion of
closure-phase, especially as it is used in the context of non-redundant Fizeau
interferometry, but extends its application to pupils of arbitrary shape, for
diffraction limited images. The additional calibration brought by kernel-phase
boosts the resolution of conventional images and enables the detection of
otherwise hidden faint features at the resolution limit and beyond, a regime
often refered to as super-resolution, which for a 30-meter telescope in the
near IR, this translates into a resolving power smaller than 10 mas.
Kernel-phase analysis of archival space and ground based AO data leads to new
discoveries and/or improved relative astrometry and photometry. The paper
presents the current status of the technique and some of its recent
developments and applications that lead to recommendations for super-resolution
imaging with ELTs.
