  Total Generalized Variation (TGV) has recently been introduced as penalty
functional for modelling images with edges as well as smooth variations. It can
be interpreted as a "sparse" penalization of optimal balancing from the first
up to the $k$-th distributional derivative and leads to desirable results when
applied to image denoising, i.e., $L^2$-fitting with TGV penalty. The present
paper studies TGV of second order in the context of solving ill-posed linear
inverse problems. Existence and stability for solutions of Tikhonov-functional
minimization with respect to the data is shown and applied to the problem of
recovering an image from blurred and noisy data.
