  Total Generalized Variation (TGV) regularization in image reconstruction
relies on an infimal convolution type combination of generalized first- and
second-order derivatives. This helps to avoid the staircasing effect of Total
Variation (TV) regularization, while still preserving sharp contrasts in
images. The associated regularization effect crucially hinges on two parameters
whose proper adjustment represents a challenging task. In this work, a bilevel
optimization framework with a suitable statistics-based upper level objective
is proposed in order to automatically select these parameters. The framework
allows for spatially varying parameters, thus enabling better recovery in
high-detail image areas. A rigorous dualization framework is established, and
for the numerical solution, two Newton type methods for the solution of the
lower level problem, i.e. the image reconstruction problem, and two bilevel TGV
algorithms are introduced, respectively. Denoising tests confirm that
automatically selected distributed regularization parameters lead in general to
improved reconstructions when compared to results for scalar parameters.
