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Image Reconstruction

Gengsheng Lawrence Zeng
Walter de Gruyter
Publication Date: 
Number of Pages: 
De Gruyter Graduate
[Reviewed by
Allen Stenger
, on

This is a brief handbook of mathematical methods for analyzing the results of various kinds of tomography scans used in medicine, including CAT, PET, and MRI. The methods are primarily based on Fourier analysis. The back-cover blurb says the book is “written in a non-mathematical way”, but take this with a grain of salt: it is full of mathematics, although it only gives the methods and not the proofs.

The book is aimed at engineers rather than mathematicians. The prerequisites are not stated, but seem to be a good understanding of Fourier series and integrals. The book also seems to assume some knowledge of signal processing: it talks about rebinning and windowing without giving any explanation of them.

The structure and exposition are very good. Each chapter has a one-page summary that really does capture all the key points of the chapter. There are good explanations of all the scanning methods and how the physics works and how they are implemented. The book gives several alternate algorithms for processing the data, and gives good explanations of their strengths and weaknesses. Then the actual mathematical formulas are gathered together in each chapter in a “Mathematical Expressions” section. The book is skimpy on exercises, and they seem to vary greatly in difficulty. There are no computer codes given, except for a few examples in MATLAB.

Allen Stenger is a math hobbyist and retired software developer. He is an editor of the Missouri Journal of Mathematical Sciences. His personal web page is His mathematical interests are number theory and classical analysis.

See the table of contents in the publisher's webpage.