Integrated PET/MR systems are becoming increasingly popular in clinical and research applications. Quantitative PET reconstruction requires correction for γ-photon attenuations using an attenuation coefficient map (μ map) that is a measure of the electron density. One challenge of PET/MR, in contrast to PET/CT, lies in the accurate computation of μ maps. Unlike CT, MR imaging measures physical properties not directly related to electron density. Previous approaches have computed the attenuation coefficients using a segmentation of MR images or using deformable registration of atlas CT images to the space of the subject MR images. In this work, we propose a patch-based method to generate whole-head μ maps from ultrashort echo-time (UTE) MR imaging sequences. UTE images are preferred to other MR sequences because of the increased signal from bone. To generate a synthetic CT image, we use patches from a reference dataset, which consists of dual-echo UTE images and a coregistered CT scan from the same subject. Matching of patches between the reference and target images allows corresponding patches from the reference CT scan to be combined via a Bayesian framework. No registration or segmentation is required. For evaluation, UTE, CT, and PET data acquired from 5 patients under an institutional review board-approved protocol were used. Another patient (with UTE and CT data only) was selected to be the reference to generate synthetic CT images for these 5 patients. PET reconstructions were attenuation-corrected using the original CT, our synthetic CT, Siemens Dixon-based μ maps, Siemens UTE-based μ maps, and deformable registration-based CT. Our synthetic CT-based PET reconstruction showed higher correlation (average ρ = 0.996, R(2) = 0.991) to the original CT-based PET, as compared with the segmentation- and registration-based methods. Synthetic CT-based reconstruction had minimal bias (regression slope, 0.990), as compared with the segmentation-based methods (regression slope, 0.905). A peak signal-to-noise ratio of 35.98 dB in the reconstructed PET activity was observed, compared with 29.767, 29.34, and 27.43 dB for the Siemens Dixon-, UTE-, and registration-based μ maps. A patch-matching approach to synthesize CT images from dual-echo UTE images leads to significantly improved accuracy of PET reconstruction as compared with actual CT scans. The PET reconstruction is improved over segmentation- (Dixon and Siemens UTE) and registration-based methods, even in subjects with pathologic findings.