Medical imaging is a very important application area of advanced computational techniques. Without the use of up-to-date mathematical ideas and the corresponding algorithms, it would not be possible to convert the measurement data coming out of today’s imaging hardware into the high-quality images we are used to seeing. A book that provides an elementary introduction to the mathematical background of such systems is therefore most welcome. Regrettably, Feeman’s book only partially succeeds in this respect.

Specifically, medical imaging specialists nowadays use a large number of technically very different techniques such as computerized tomography (CT), magnetic resonance imaging (MRI), positron emission tomography (PET), single-photon emission computed tomography (SPECT), ultrasonography, and so on. Except for a very small chapter dealing with MRI, the book only covers the CT method, whereas all other techniques are not discussed at all. While this fact renders the book’s title somewhat inaccurate, it is clearly mentioned in the cover text, so it does not completely surprise the reader.

The description of CT that Feeman provides is appropriate for a book written for beginners and readers without a strong mathematical background. The mathematical level is elementary, but plenty of pointers to advanced literature are given for readers who want to know more details. Feeman covers all relevant aspects of CT; a particularly useful feature is that the descriptions of the algorithms required to implement CT methods are accompanied by code snippets written not in some pseudocode, but in a real programming language. However, the language of Feeman’s choice is R, a language developed for statistical applications, which does not appear to be the most natural choice for imaging algorithms. Presumably, it is also not a language with which most of the potential readers will be familiar.

A book with such a topic and technical level clearly requires a carefully chosen set of graphical illustrations. Except for a small part in chapter 7 that would have benefited if more pictures had been included, Feeman’s selection of figures is totally satisfactory. I also found a remarkably small number of misprints and incorrect cross-references; when a book is written for a readership that essentially consists of novices, this is an important feature.

In spite of the shortcomings mentioned above, I believe that the book is a useful starting point for undergraduate students from mathematics, computer science, and related fields who want to learn how CT works; it also provides interesting reading for people from medical areas who want to find out the technical and mathematical background of the tools that they use.

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