Inversion of Weighted Divergent Beam and Cone Transforms

TL;DR

This paper derives new inversion formulas for weighted divergent beam and cone transforms, which are useful in imaging applications like Compton cameras, with numerical results in 2D and 3D.

Contribution

It introduces novel inversion formulas for weighted divergent beam and cone transforms, expanding their applicability across various detector geometries and dimensions.

Findings

Derived inversion formulas applicable in any dimension.

Numerical implementation results in 2D and 3D.

Enhanced understanding of relations between Radon and cone transforms.

Abstract

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.