The Radon Transform

Part of the Springer Undergraduate Texts in Mathematics and Technology book series (SUMAT)


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 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 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.


Image Reconstruction Fundamental Question Constant Density Computer Algebra System Attenuation Function 
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Copyright information

© Springer-Verlag New York 2010

Authors and Affiliations

  1. 1.Department of Mathematical SciencesVillanova UniversityVillanovaUSA

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