Prediction of CT Substitutes from MR Images Based on Local Diffeomorphic Mapping for Brain PET Attenuation Correction

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Abstract
Attenuation correction is important for PET (positron emission tomography) reconstruction. In PET/MR (magnetic resonance), MR intensities are not directly related to attenuation coefficients that are needed in PET imaging. The attenuation coefficient map can be derived from CT (computed tomography) images. Therefore, prediction of CT substitutes from MR images is desired for attenuation correction in PET/MR. Methods: This study presents a patch-based method for CT prediction from MR images, generating attenuation maps for PET reconstruction. Since no global relation exists between MR and CT intensities, we propose local diffeomorphic mapping (LDM) for CT prediction. In LDM, we assume that MR and CT patches are located on two nonlinear manifolds and the mapping from the MR manifold to the CT manifold approximates a diffeomorphism under a local constraint. Locality is important in LDM and is constrained by the following techniques. First is local dictionary construction, wherein, for each patch in the testing MR image, a local search window is used to extract patches from training MR/CT pairs to construct MR and CT dictionaries. The k-nearest neighbors and an outlier detection strategy are then used to constrain the locality in MR and CT dictionaries. Second is local linear representation, wherein, local anchor embedding is used to solve MR dictionary coefficients when representing the MR testing sample. Under these local constraints, dictionary coefficients are linearly transferred from the MR manifold to the CT manifold, and used to combine CT training samples to generate CT predictions. Results: Our dataset contains 13 healthy subjects, each with T1- and T2-weighted MR and CT brain images. This method provides CT predictions with a mean absolute error of 110.1 Hounsfield units, Pearson's linear correlation of 0.82, peak signal-to-noise ratio of 24.81 dB, and Dice in bone regions of 0.84 as compared to real CTs. CT substitute based PET reconstruction has a regression slope of 1.0084 and R2 of 0.9903 compared to real CT based PET. Conclusion: In this method, no image segmentation or accurate registration is required. Our method demonstrates superior performance in CT prediction and PET reconstruction compared to competing methods.

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