The objective of this crash course is to introduce and discuss mathematical models for the data formation process in medical imaging and computational methods for the numerical reduction of such models. The syllabus of the course could read as follows:
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Overview of medical imaging modalities.
Overview of mathematical models.
Overview of computational methods.
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Structural imaging – X-ray tomography.
The Radon Transform and its inversion.
Uniqueness and stability issues.
Imaging methods.
Filtered Back Projection.
Expectation Maximization.
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Structural imaging – magnetic resonance imaging.
The signal formation model.
Fourier-based imaging.
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Functional imaging – Parametric imaging.
Tracers and tracer kinetics.
Compartmental models.
Uniqueness issues.
Inversion methods.
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Functional imaging – neurophysiology.
Signal formation models in EEG and MEG.
Source modelling.
Connectivity issues.
Artificial intelligence for patients’ stratification.
