Free discontinuity problems and image inpainting

Several variational problems related to image analysis have been
studied in recent years. This talk focuses on functionals coupling bulk energy depending on second order derivatives of the admissible
functions, and surface energy due to discontinuity and gradient discontinuity. The case of vector-valued admissible functions is considered too, in order to analyze RGB color images.
As an application to image analysis, we discuss the problem
of inpainting, say the reconstruction in the whole domain of a 2-D image which is damaged or even completely lost in a small subdomain.