Joint reconstruction via coupled Bregman iterations with applications to PET-MR imaging

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.