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This work describes a procedure to yield attenuation maps from MR images which are used for the absorption correction (AC) of brain PET data. Such an approach could be mandatory for future combined PET and MRI scanners, which probably do not include a transmission facility. T1-weighted MR images were segmented into brain tissue, bone, soft tissue, and sinus; attenuation coefficients corresponding to elemental composition and density as well as to 511 keV photon energy were respectively assigned. Attenuation maps containing up to four compartments were created and forward projected into sinograms with attenuation factors which then were used for AC during reconstruction of FDG-PET data. The commonly used AC based on a radioactive (68Ge) transmission scan served as reference. The reconstructed radioactivity values obtained with the MRI-based AC were about 20% lower than those obtained with PET-based AC if the skull was not taken into account. Considering the skull the difference was still about 10%. Our investigations demonstrate the feasibility of a MRI-based AC, but revealed also the necessity of a satisfying delineation of bone thickness which tends to be underestimated in our first approach of T1-weighted MR image segmentation.