Alzheimer's Disease (AD) is the most common form of dementia, characterised by cognitive decline and biomarkers such as tau-proteins. Tau-positron emission tomography (tau-PET), which employs a radiotracer to selectively bind, detect, and visualise tau protein aggregates within the brain, is valuable for early AD diagnosis but is less accessible due to high costs, limited availability, and its invasive nature. Image synthesis with neural networks enables the generation of tau-PET images from more accessible T1-weighted magnetic resonance imaging (MRI) images. To ensure high-quality image synthesis, we propose a cyclic 2.5D perceptual loss combined with mean squared error and structural similarity index measure (SSIM) losses. The cyclic 2.5D perceptual loss sequentially calculates the axial 2D average perceptual loss for a specified number of epochs, followed by the coronal and sagittal planes for the same number of epochs. This sequence is cyclically performed, with intervals reducing as the cycles repeat. We conduct supervised synthesis of tau-PET images from T1w MRI images using 516 paired T1w MRI and tau-PET 3D images from the ADNI database. For the collected data, we perform preprocessing, including intensity standardisation for tau-PET images from each manufacturer. The proposed loss, applied to generative 3D U-Net and its variants, outperformed those with 2.5D and 3D perceptual losses in SSIM and peak signal-to-noise ratio (PSNR). In addition, including the cyclic 2.5D perceptual loss to the original losses of GAN-based image synthesis models such as CycleGAN and Pix2Pix improves SSIM and PSNR by at least 2% and 3%. Furthermore, by-manufacturer PET standardisation helps the models in synthesising high-quality images than min-max PET normalisation.

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