Exploiting the Ranges of Radon Transformsin Tomography

  • Frank Natterer
Part of the Progress in Scientific Computing book series (PSC, volume 2)


The classical Radon transform of a function f with support in the unit disc Ω of IR2 is defined as
$${\rm{Rf(s,\omega )}}\;{\rm{ = }}\;\int\limits_{{\rm{x}}{\rm{\omega }} = {\rm{s}}} {{\rm{f(x)dx}}\;{\rm{ = }}} \;\int {{\rm{f(s\omega }}\;{\rm{ + }}\;{\rm{t}}{{\rm{\omega }}^{\rm{\perp }}}{\rm{)}}\;{\rm{dt}}}$$
Here, s ε IR1 and ω= (cos ϕ, s in ϕ), ω = (−sin ϕ, cos ϕ), o ≤ ϕ < 2π. Thus, R associates with each f the set of its line integrals.


Chebyshev Polynomial Homogeneous Polynomial Source Distribution Line Integral Radon Transform 
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Copyright information

© Birkhäuser Boston 1983

Authors and Affiliations

  • Frank Natterer

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