INVERSION OF WEIGHTED DIVERGENT BEAM AND CONE TRANSFORMS Academic Article

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.

authors

• Kuchment, Peter

published proceedings

• INVERSE PROBLEMS AND IMAGING

author list (cited authors)

• Kuchment, P., & Terzioglu, F.

citation count

• 21

complete list of authors

• Kuchment, Peter||Terzioglu, Fatma

publication date

• December 2017

publisher

• American Institute of Mathematical Sciences (AIMS)  Publisher

published in

• Inverse Problems and Imaging  Journal

keywords

• Compton Camera
• Imaging
• Integral Geometry
• Inversion
• Radon Transform
• Weighted Cone Transform
• Weighted Divergent Beam Transform

Digital Object Identifier (DOI)

• 10.3934/ipi.2017049

start page

• 1071

end page

• 1090

volume

• 11

issue

• 6

URL

• http://dx.doi.org/10.3934/ipi.2017049