Novikov ’ s Inversion Formula for the Attenuated Radon Transform — A New Approach

We study the inversion of weighted Radon transforms in two dimensions,Rρf (L) = ∫ L f (·) ρ(L, ·) ds, where the weight function ρ(L, x), L a line and x ∈ L, has a special form. It was an important breakthrough when R.G. Novikov recently gave an explicit formula for the inverse of Rρ when ρ has the form (1.2); in this case Rρ is called the attenuated Radon transform. Here we prove similar results for a somewhat larger class of ρ using completely different and quite elementary methods.