Inversion of weighted divergent beam and cone transforms Academic Article uri icon

abstract

  • 2017 American Institute of Mathematical Sciences. In this paper, we investigate the relations between the Radon and weighted divergent beam and cone transforms. Novel inversion formulas are derived for the latter two. The weighted cone transform arises, for instance, in image reconstruction from the data obtained by Compton cameras, which have promising applications in various fields, including biomedical and homeland security imaging and gamma ray astronomy. The inversion formulas are applicable for a wide variety of detector geometries in any dimension. The results of numerical implementation of some of the formulas in dimensions two and three are also provided.

published proceedings

  • Inverse Problems & Imaging

author list (cited authors)

  • Kuchment, P., & Terzioglu, F.

citation count

  • 16

complete list of authors

  • Kuchment, Peter||Terzioglu, Fatma

publication date

  • January 2017