Math Colloquia: Linh V. Nguyen (University of Idaho)
Monday, September 12 2011
Math Colloquia, presented by Linh V. Nguyen (University of Idaho), "Range description for a spherical mean transform" will occur Sept. 15 at 3:30 p.m. in TLC 030.
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.