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On Local Injectivity for Generalized Radon Transforms

  • Jan Boman
Conference paper
Part of the Springer Proceedings in Mathematics book series (PROM, volume 16)

Abstract

We consider a class of weighted plane generalized Radon transforms Rf(γ)=∫f(x,u(ξ,η,x))m(ξ,η,x) dx, where the curve γ=γ (ξ,η) is defined by y=u(ξ,η,x), and m(ξ,η,x) is a given positive weight function. We prove local injectivity for this transform across a given curve γ 0 near a given point (x 0,y 0) on γ 0 for classes of curves and weight functions that are invariant under arbitrary smooth coordinate transformations in the plane.

Keywords

Weight Function Local Injectivity Radon Transform Local Diffeomorphisms Curve Family 
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Copyright information

© Springer-Verlag Italia 2012

Authors and Affiliations

  1. 1.Stockholm UniversityStockholmSweden

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