The reconstruction of PET brain data in a PET/MR hybrid scanner is challenging in the absence of transmission sources, where MR images are used for MR-based attenuation correction (MR-AC). The main challenge of MR-AC is to separate bone and air, as neither have a signal in traditional MR images, and to assign the correct linear attenuation coefficient to bone. The ultra-short echo time (UTE) MR sequence was proposed as a basis for MR-AC as this sequence shows a small signal in bone. The purpose of this study was to develop a new clinically feasible MR-AC method with patient specific continuous-valued linear attenuation coefficients in bone that provides accurate reconstructed PET image data. A total of 164 [(18)F]FDG PET/MR patients were included in this study, of which 10 were used for training. MR-AC was based on either standard CT (reference), UTE or our method (RESOLUTE). The reconstructed PET images were evaluated in the whole brain, as well as regionally in the brain using a ROI-based analysis. Our method segments air, brain, cerebral spinal fluid, and soft tissue voxels on the unprocessed UTE TE images, and uses a mapping of R(*)2 values to CT Hounsfield Units (HU) to measure the density in bone voxels. The average error of our method in the brain was 0.1% and less than 1.2% in any region of the brain. On average 95% of the brain was within  ±10% of PETCT, compared to 72% when using UTE. The proposed method is clinically feasible, reducing both the global and local errors on the reconstructed PET images, as well as limiting the number and extent of the outliers.