On the Determination of Star Bodies from Their Half-Sections

TL;DR

This paper develops explicit inversion formulas for a Radon-like transform involving hemispherical integrals, enabling the reconstruction of star bodies from their central half-section volumes.

Contribution

It introduces new explicit inversion formulas for a Radon-like transform related to hemispherical integrals, aiding in star body reconstruction.

Findings

Derived explicit inversion formulas for the transform.

Applied formulas to determine star bodies from half-section volumes.

Enhanced understanding of geometric tomography methods.

Abstract

We obtain explicit inversion formulas for the Radon-like transform that assigns to a function on the unit sphere the integrals of that function over hemispheres lying in lower dimensional central cross-sections. The results are applied to determination of star bodies from the volumes of their central half-sections.