ABSTRACT
This chapter deals with analytical methods for image reconstruction. Practical algorithms are then obtained by finding an analytical inversion formula for the continuous-space projection function, followed by a discretisation of an inverted transform. In Computed Tomography (CT), two dimension (2D) analytical reconstruction is employed both on first generations of multi-detector CT systems, as well as in helical CT; in Positron Emission Tomography, the problem of 3D reconstruction is very often reduced to a set of 2D problems by using specialized techniques to rebin the oblique LOR’s on a set of 2D sinograms. In fact, analytical methods have the big advantage of being less computationally intensive, as compared to iterative ones, and they are generally easy to implement.
