Department of Mathematics Colloquium

University of Idaho

Fall 2011
Thursday,  September 15, 3:30-4:20pm, room TLC 030

Refreshments in Brink 305 at 3:00 p.m.

Range description for a spherical mean transform

 

Linh Nguyen


Department of Mathematics

University of Idaho



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.