An analytical inversion formula for the overdetermined spherical section transform
Year: 2025
Type: article
Abstract: This paper addresses the inversion of the overdetermined spherical section transform, which integrates a function defined on the unit sphere in R n over the full set of ( n − 2 ) -dimensional subspheres obtained by intersecting the unit sphere with hyperplanes in R n . The inversion of the spherical section transform and its variants have applications in various tomographic imaging techniques, including thermoacoustic and photoacoustic tomography, as well as Compton camera imaging. We derive analytic inversion formulas for the overdetermined spherical section transform in n-dimensions and demonstrate the stability of inversion in three dimensions.
Source: Inverse Problems
Author: Fatma Terzioglu
Institution: North Carolina State University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,325
Award: G6837600482
OpenAlex ID: W4413820866