chapter  1
20 Pages

Radon Transform

Let E be an Euclidean space of dimension n > 1 with the scalar product 〈·, ·〉 . We denote by H(p, ω) the hyperplane of E given by equation 〈ω, x〉 = p, where ω is a unit vector in E and p ∈ R. This parameterization is two-sheeted, since H (−p,−ω) = H (p, ω). The Radon transform of an integrable function f on E is the family of its integrals over the hyperplanes H = H (p, ω),

Rf(H) . =

∫ H

fdH, Rf(p, ω) =

∫ H(p,ω)

fdH.