Inside Out: Inverse Problems and Applications (Mathematical Sciences Research Institute Publications, Series Number 47)

There have been substantial developments in the mathematical theory of inverse problems over the last twenty years and applications have expanded greatly in medical imaging, geophysical exploration, and non-destructive evaluation. In this book, leading experts in the theoretical and applied aspects of inverse problems offer extended surveys on several important topics in the field, such as microlocal analysis, reflection seismology, tomography, inverse scattering, and X-ray transforms.

"It's safe to say that Uhlmann's book is a fingerpost in mathematical imaging for some time to come."
Bulletin of the American Mathematical Society