For quantitative PET information, correction of tissue photon attenuation is mandatory. Generally in conventional PET, the attenuation map is obtained from a transmission scan, which uses a rotating radionuclide source, or from the CT scan in a combined PET/CT scanner. In the case of PET/MRI scanners currently under development, insufficient space for the rotating source exists; the attenuation map can be calculated from the MR image instead. This task is challenging because MR intensities correlate with proton densities and tissue-relaxation properties, rather than with attenuation-related mass density. Methods: We used a combination of local pattern recognition and atlas registration, which captures global variation of anatomy, to predict pseudo-CT images from a given MR image. These pseudo-CT images were then used for attenuation correction, as the process would be performed in a PET/CT scanner. Results: For human brain scans, we show on a database of 17 MR/CT image pairs that our method reliably enables estimation of a pseudo-CT image from the MR image alone. On additional datasets of MRI/PET/CT triplets of human brain scans, we compare MRI-based attenuation correction with CT-based correction. Our approach enables PET quantification with a mean error of 3.2% for predefined regions of interest, which we found to be clinically not significant. However, our method is not specific to brain imaging, and we show promising initial results on 1 whole-body animal dataset. Conclusion: This method allows reliable MRI-based attenuation correction for human brain scans. Further work is necessary to validate the method for whole-body imaging.

PET/MRI is an emerging dual-modality imaging technology that requires new approaches to PET attenuation correction (AC). We assessed 2 algorithms for whole-body MRI-based AC (MRAC): a basic MR image segmentation algorithm and a method based on atlas registration and pattern recognition (AT&PR). Methods: Eleven patients each underwent a whole-body PET/CT study and a separate multibed whole-body MRI study. The MR image segmentation algorithm uses a combination of image thresholds, Dixon fat–water segmentation, and component analysis to detect the lungs. MR images are segmented into 5 tissue classes (not including bone), and each class is assigned a default linear attenuation value. The AT&PR algorithm uses a database of previously aligned pairs of MRI/CT image volumes. For each patient, these pairs are registered to the patient MRI volume, and machine-learning techniques are used to predict attenuation values on a continuous scale. MRAC methods are compared via the quantitative analysis of AC PET images using volumes of interest in normal organs and on lesions. We assume the PET/CT values after CT-based AC to be the reference standard. Results: In regions of normal physiologic uptake, the average error of the mean standardized uptake value was 14.1% ± 10.2% and 7.7% ± 8.4% for the segmentation and the AT&PR methods, respectively. Lesion-based errors were 7.5% ± 7.9% for the segmentation method and 5.7% ± 4.7% for the AT&PR method. Conclusion: The MRAC method using AT&PR provided better overall PET quantification accuracy than the basic MR image segmentation approach. This better quantification was due to the significantly reduced volume of errors made regarding volumes of interest within or near bones and the slightly reduced volume of errors made regarding areas outside the lungs.

We study nonparametric regression between Riemannian manifolds based on regularized empirical risk minimization. Regularization functionals for mappings between manifolds should respect the geometry of input and output manifold and be independent of the chosen parametrization of the manifolds. We define and analyze the three most simple regularization functionals with these properties and present a rather general scheme for solving the resulting optimization problem. As application examples we discuss interpolation on the sphere, fingerprint processing, and correspondence computations between three-dimensional surfaces. We conclude with characterizing interesting and sometimes counterintuitive implications and new open problems that are specific to learning between Riemannian manifolds and are not encountered in multivariate regression in Euclidean space.