Display Abstract

Title Universal Inversion Formulas for Recovering a Function from Spherical Means

Name Markus Haltmeier
Country Austria
Email markus.haltmeier@uibk.ac.at
Submit Time 2014-02-08 12:36:00
Special Session 45: Hybrid imaging methods
In this talk we derive universal back-projection type reconstruction formulas for recovering a function in arbitrary dimension from averages over spheres centered on the boundary of a bounded convex domain with smooth boundary. Provided that the unknown function is supported inside that domain, the derived formulas recover the unknown function up to an explicitly computed integral operator. For elliptical domains the integral operator is shown to vanish and hence we establish exact inversion formulas for recovering a function from spherical means centered on the boundary of elliptical domains in arbitrary dimension.