For someone with a little background and a lot of determination, this book provides a good basic grounding in the issues of tomographic reconstruction and the basic mathematical tools involved. Discussion starts slowly, with a chapter that establishes the vocabulary and notation of the signal processing involved. The next three chapters discuss non-diffracting cases, where the radiation that senses the body structures is not appreciably deflected by them, as is the case for CAT, PET, and SPECT. This includes discussion of the sensors, illuminators, and their geometries, on up to helical scans and complex sensor geometries. It also includes confounding effects, like the wavelength dependent nonlinearities in absorption of X-rays and how they affect beam transmission and the final image produced.

This chapter includes only brief menton of MRI, because of the very different physics behind it, and of ultrasonography, because of the diffractive and refractive features of the radiator and tissues being examined. Likewise, little mention is made of the reasons for different modalities or techniques for merging their results.

The final chapters address the special problems of ultrasound, digging as far in as the wave equations and the common approximations that make the wave equations at least somewhat practical as tools for solution. These chapters also address more advanced and computationally exhorbitant algorithms, though not in nearly the detail that back-projection got in the earlier chapters.

This book first appeared in 1988, which seems like centuries ago in the time scale of tomography algorithm development. Even the 2001 update is aging, and it never really went into the Feldkamp algorithms now widely in use. The discussion of sonography seems sketchier than discussion of the X-ray based modalities, and MRI newer exotica get little if any attention. That's fine, though. It's a big field, and the authors do reasonably well at defining and addressing the area they intended to cover. The working algorithm developer won't get much from this classic. The target audience today is probably a grad student or industrial practitioner who's been thrown in at the deep end. As long as its limits remain clear, this is a helpful introduction for readers with the math skills and time needed to extract its value.

— wiredweird