Respiratory motion leads to motion blurring of PET images and thus an underestimation of the reconstructed activity. Recent approaches for PET/MR motion compensation use 3 to 10 minutes of MR acquisition time per bed position¹. To allow for MR acquisition times as short as 1 minute per bed, we propose a new method for PET/MR respiratory motion compensation (MoCo) that employs strongly undersampled MR data.Simultaneous PET/MR data covering the thorax of three free-breathing patients diagnosed with lung cancer were acquired at a Biograph mMR system (Siemens Healthcare, Erlangen, Germany). Data acquisition and evaluation was in accordance with the local ethics committee and informed consent was obtained from each patient. We applied a vendor-provided radial stack-of-stars sequence with golden angle radial spacing and sagittal slice orientation: field-of-view: 400×400×396 mm³, voxel size: 1.6×1.6×4.5 mm³, TR/TE = 3.75/1.70 ms, 88 slices (55% slice resolution, 6/8 partial Fourier), flip angle: 10°, fat supression activated. For PET imaging the radionuclide fluorodeoxyglucose (¹⁸F-FDG) was used and the acquisition time was 300 s per bed. MR data and PET list-mode data were sorted retrospectively into 20 overlapping respiratory motion phase bins with a width of 10% employing an intrinsic MR motion surrogate signal. For motion estimation, only MR data measured within the first 60 s of the data acquisition were used (Fig. 1). These data corresponded to 36 radial spokes per slice and motion phase and an undersampling factor of 11.2. Motion vector fields (MVFs) were estimated with a newly-developed algorithm, which alternates between MR image reconstruction and motion estimation. To increase the robustness, deformable registrations were carried out between adjacent motion phases in a cyclic manner, and these were further regularized by cyclic constraints². Standard 4D gated gridding and 4D MoCo MR reconstructions were performed, with the latter incorporating the estimated MVFs. In addition, 3D PET and 4D gated PET images were generated with a standard OSEM algorithm. For 4D MoCo PET reconstructions, MVFs derived from MR were incorporated into the system matrix³. For all PET reconstructions, 3 iterations with 21 subsets were used and a Gaussian smoothing filter (FWHM = 3.2 mm) was applied at the end of each iteration.For demonstration purposes, different motion phases of 4D gated gridding MR and 4D MoCo MR reconstructions are shown in Fig. 2. 4D gated gridding MR images revealed severe streak artifacts and high noise levels. Both artifacts and noise were reduced considerably in the 4D MoCo MR images while the motion information was fully preserved. Figure 3 presents different PET image reconstructions of an end-exhale motion phase. 3D PET showed an increased lesion size due to motion blurring while 4D gated PET yielded an increased noise level. 4D MoCo PET images were only slightly affected by these two sources of uncertainty. For quantitative evaluation, SUV_mean values were measured for three lung lesions of the patients. Compared to 3D PET, SUV_mean values of 4D gated PET and 4D MoCo PET were 3.0% and 9.1% larger on average while standard deviations were 81.0% and 9.6% larger on average, respectively. These findings demonstrate that 4D MoCo PET is able to reduce the underestimation of activity due to motion blurring compared to 3D PET and to increase signal-to-noise ratio and contrast-to-noise ratio compared to 4D gated PET.In this study, we proposed a new respiratory motion compensation for PET images. It employs strongly undersampled MR data, which can be acquired within 1 minute. 4D MoCo PET reconstructions achieved a considerable visual and quantitative improvement compared to standard 3D PET and 4D gated PET reconstructions. By improving PET quantification and image quality, the new method can potentially increase the diagnostic value of clinical PET/MR. In addition, the remaining MR acquisition time per bed (about 4 minutes) is not needed for motion estimation and is thus available for clinical MR sequences.