Explicit inversion formulae for the spherical mean Radon transform

By Leonid A. Kunyansky. 2006

306 citations recorded by the source corpus.

We derive explicit formulae for the reconstruction of a function from its integrals over a family of spheres, or for the inversion of the spherical mean Radon transform. Such formulae are important for problems of thermo- and photo-acoustic tomography. A closed-form inversion formula of a filtration-backprojection type is found for the case when the centres of the integration spheres lie on a sphere in surrounding the support of the unknown function.

Subfields: Biomedical Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/49d54a3f04ac4464e07f30c4c1375ba44e33f79e

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In Biomedical Engineering

In Mechanics of Materials

Citations in the corpus

Mathematics of thermoacoustic tomography (2007, background): “We, however, know that such formulas have been discovered [38, 77].”
Reconstruction and time reversal in thermoacoustic tomography in acoustically homogeneous and inhomogeneous media (2008, background): “[36] L.”
Inversion of Spherical Means and the Wave Equation in Even Dimensions (2007, unknown): “Recently, Kunyansky [ 11 ] has also established inversion formulas of the filtered backprojection type for the spherical mean transform.”