In this well-written booklet the reader can find a very nice overview of those inverse problems which are under consideration in medical imaging. More generally, the book is dealt with the determination of unknown coefficients in partial differential equations of mathematical physics. Besides applications in different variants of tomography inverse problems in partial differential equations that are of interest in the book also occur in non-destructive evaluation of materials, underwater imaging, geophysical propspection and microscopy. In contrast to many other books on parameter identification in PDEs this is really an introduction which can be used to become acquainted with basic analytic and numeric aspects of tomography problems.
After an introduction presenting a series of practical examples Chapter 2 is devoted to the Radon transform, its inversion, applications to the wave equation and reconstruction methods. In Chapter 3 the Dirichlet-to-Neumann map plays the basic role. The approximate solution of the impedance tomography problem is studied in detail as an important application. In Chapter 4 discrete models of medical imaging are discussed, in particular the diffuse tomography model. An appendix on the background of functional analysis associated with inverse problems completes the booklet.