The recently introduced second order total generalised variation functional
TGVβ,α2​ has been a successful regulariser for image
processing purposes. Its definition involves two positive parameters α
and β whose values determine the amount and the quality of the
regularisation. In this paper we report on the behaviour of
TGVβ,α2​ in the cases where the parameters α,β as well as their ratio β/α becomes very large or very small.
Among others, we prove that for sufficiently symmetric two dimensional data and
large ratio β/α, TGVβ,α2​ regularisation
coincides with total variation (TV) regularisation