Even though wavelet analysis is a recent development in mathematics, the classical theory of sampling goes back to the 19th century. Similarly, the foundations of tomography date back to 1917, and were first studied by Radon; its implementation, however, is considered to be a recent development.

This book is the outcome of the Sampling Theory and Applications (SampTA) 2001 conference, which was held at the University of Central Florida in May 2001. In this work, the authors combine three research areas that could be considered at the heart of harmonic analysis; the purpose of this proceeding is to present recent developments in sampling, wavelets, and tomography, all active research areas in contemporary mathematics, with wide applications in signal processing, image processing, and computed tomography (CT) scans.

The proceedings are written by mixture of mathematicians, scientists, and engineers who are working in the signal processing and image processing fields, as well as in medical imaging. There are 12 chapters, as well as a very informative and well-written introduction by Zayed. The papers range from expository and historical surveys to original research papers on recent developments in the three focus areas. One could almost glean sufficient information about the proceedings, and the design of the proceedings, as well as its contents, by reading the first chapter.

Even though is not clearly stated, the book can be considered to be made up of four parts. Part 1 would be the introduction, by Zayed. Chapters 2, 3, and 4 address sampling, and could be considered Part 2. Part 3 would be chapters 5 through 8, focusing on the sampling in shifting subspaces of L² ℜ, and also containing some new results, such as the extension of multi-resolution analysis to abstract Hilbert space. Part 4 is made up of chapters 9 through 12, and focuses on a study of tomography, and several other sampling schemes in numerical and medical imaging.

Each chapter has its own abstract, and the authors of each chapter do a good job of presenting the links and the interconnections among sampling theory, wavelets, and tomography. The book would be suitable for mathematicians, scientists, and engineers who are working on signal processing, image processing, and medical imaging, as well as for graduate students in related areas.