  We consider the bilevel optimisation approach proposed by De Los Reyes,
Sch\"onlieb (2013) for learning the optimal parameters in a Total Variation
(TV) denoising model featuring for multiple noise distributions. In
applications, the use of databases (dictionaries) allows an accurate estimation
of the parameters, but reflects in high computational costs due to the size of
the databases and to the nonsmooth nature of the PDE constraints. To overcome
this computational barrier we propose an optimisation algorithm that by
sampling dynamically from the set of constraints and using a quasi-Newton
method, solves the problem accurately and in an efficient way.
