Department of Mathematics Colloquium


Abstract 

Spherical mean transform sends a function to
its mean values on spheres. This transform has important applications
in many areas, such as PDEs, biomedical and geophysical imaging, and
approximation theory. In practice, one normally deals with the
restrictions of spherical mean transform to some specific sets of
spheres. In this talk, we will discuss one such restriction arising
thermoacoustic/photoacoustic tomography, a new modality of biomedical
imaging. We will present the range description of the transform. We
will also generalize the result to the spaces of constant
curvatures.
