For a mathematician, however, the main motivation for working
on these various tomographic modalities is that they bring about a
large variety of challenging and beautiful mathematical problems that
involve more or less all areas of mathematics.
http://arxiv.org/abs/1107.2447
The article provides a brief survey of the mathematics of some of the newly
being developed so called "hybrid" (also called "multi-physics" or
"multi-wave") imaging techniques.
Along with a list of the main mathematical problems in TAT