DisQ-HNet: A Disentangled Quantized Half-UNet for Interpretable Multimodal Image Synthesis Applications to Tau-PET Synthesis from T1 and FLAIR MRI

Tau positron emission tomography (tau-PET) provides an in vivo marker of Alzheimer's disease pathology, but cost and limited availability motivate MRI-based alternatives. We introduce DisQ-HNet (DQH), a framework that synthesizes tau-PET from paired T1-weighted and FLAIR MRI while exposing how each modality contributes to the prediction. The method combines (i) a Partial Information Decomposition (PID)-guided, vector-quantized encoder that partitions latent information into redundant, unique, and complementary components, and (ii) a Half-UNet decoder that preserves anatomical detail using pseudo-skip connections conditioned on structural edge cues rather than direct encoder feature reuse. Across multiple baselines (VAE, VQ-VAE, and UNet), DisQ-HNet maintains reconstruction fidelity and better preserves disease-relevant signal for downstream AD tasks, including Braak staging, tau localization, and classification. PID-based Shapley analysis provides modality-specific attribution of synthesized uptake patterns.