| Contents | Positron emission tomography (PET) becomes quantitative only through mathematical modeling. This talk follows that pipeline from the forward model of image formation to three applications. First, compartmental ODE and reference- region models quantify [¹¹C]DPA713 binding as a marker of neuroinflammation in multiple sclerosis, without arterial sampling. Second, deep learning on FDG-PET, which fuses voxel- and region-level features, improves Alzheimer's disease classification. Third, partial volume correction is treated as an ill- posed inverse problem, with Van Cittert, re-blurred Van Cittert, and Richardson–Lucy iterations read as Neumann, Landweber, and EM schemes, where the iteration number acts as the regularization parameter, and corrected images change the performance of CNN and PCANet classifiers. Together, these studies show where applied mathematics enters quantitative neuroimaging: in models, learning, and inversion.
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