Biomedical Imaging

4Tomography

This chapter presents the fundamental concepts of computerized tomography (CT). CT provides three-dimensional (3d) reconstructions of objects or bodies from a series of different views (exposures), each at a different angle. More precisely, the spatial distribution of an observable f is reconstructed in n-dimensional space from projections into (n−1)-dimensional subspaces. The observable f can, for example, represent the electron density, the mass density, the x-ray attenuation coefficient, a radioactive tracer density, a fluorescence intensity and so forth, depending on the type of tomographic recording. Importantly, each projection must be given by an integral over a set of parallel hyperplanes. In 2d, the data must, hence, be given ...