The Mathematics of Medical Imaging pp 11-18 | Cite as

# 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*.

## Keywords

Image Reconstruction Fundamental Question Constant Density Computer Algebra System Attenuation Function## Preview

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