The Radon Transform

Abstract

For a given function f defined in the plane, which may represent, for instance, the attenuation-coefficient function in a cross section of a sample, the fundamental question of image reconstruction calls on us to consider the value of the integral of f along a typical line ℓ _t , θ. For each pair of values of t and θ, we will integrate f along a different line. Thus, we really have a new function on our hands, where the inputs are the values of t and θ and the output is the value of the integral of f along the corresponding line ℓ _t , θ. But even more is going on than that because we also wish to apply this process to a whole variety of functions f . So really we start by selecting a function f . Then, once f has been selected, we get a corresponding function of t and θ.