This research derives analytic inversion formulas for the spherical section transform, suggesting potential applications in tomographic imaging methods.
This paper addresses the inversion of the overdetermined spherical section transform, which integrates a function defined on the unit sphere in Rⁿ over the full set of $(n−2)$-dimensional subspheres obtained by intersecting the unit sphere with hyperplanes in Rⁿ. 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.
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Fatma Terzioglu (2025) studied this question.
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