  A novel class of semi-norms, generalising the notion of the isotropic total
variation $TV_{2}$ and the an-isotropic total variation $TV_{1}$ is introduced.
A supervised learning method via bilevel optimisation is proposed for the
computation of optimal parameters for this class of regularizers. Existence of
solutions to the bilevel optimisation approach is proven. Moreover, a
finite-dimensional approximation scheme for the bilevel optimisation approach
is introduced that can numerically compute a global optimizer to any given
accuracy.
