  Joint reconstruction has recently attracted a lot of attention, especially in
the field of medical multi-modality imaging such as PET-MRI. Most of the
developed methods rely on the comparison of image gradients, or more precisely
their location, direction and magnitude, to make use of structural similarities
between the images. A challenge and still an open issue for most of the methods
is to handle images in entirely different scales, i.e. different magnitudes of
gradients that cannot be dealt with by a global scaling of the data. We propose
the use of generalized Bregman distances and infimal convolutions thereof with
regard to the well-known total variation functional. The use of a total
variation subgradient respectively the involved vector field rather than an
image gradient naturally excludes the magnitudes of gradients, which in
particular solves the scaling behavior. Additionally, the presented method
features a weighting that allows to control the amount of interaction between
channels. We give insights into the general behavior of the method, before we
further tailor it to a particular application, namely PET-MRI joint
reconstruction. To do so, we compute joint reconstruction results from blurry
Poisson data for PET and undersampled Fourier data from MRI and show that we
can gain a mutual benefit for both modalities. In particular, the results are
superior to the respective separate reconstructions and other joint
reconstruction methods.
