Part I: X-ray tomography (overview); Radon transform,formulas for the inversion of the Radontransform (as back projection and filtered back projection), issues of uniqueness.
Part II: positron emission tomography (overview); on the two inverse problems related to positronemission tomography: an imaging problem (inversion of the Radon transform) and a compartmentalone (Gauss-Newton optimization scheme)
Part III: magnetic resonance imaging (overview); models for data acquisition and magnetic fielddistortion, Fourier transform, inversion of the Fourier transform from undersampled data.