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The Mathematics of Computerized Tomography (Classics in Applied Mathematics)

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For the student of the Radon transform and its many applications, this book is a must. It's all here: the Radon transform in a multidimensional setting, the X-ray transform (a closely related transform), general theorems for the Fourier transform of the Radon transform, and theorems on the range of the Radon transform. The author also covers sampling theorems, ill-posed problems, orthogonal functions, and tomography for incomplete sampling. He also offers much material on other allied transforms, the exponential Radon transform and the Radon transform for nonuniform attenuation, one of the major unsolved problems of mathematical physics.

This book is also an example of how a minimal and succinct notation can actually affect the way one approaches the research and thinks about problems. This is worth the price of the book alone. Nowhere else will you find such clear, brief exposition of many difficult theorems associated with the Radon transform. Initially, it is difficult to learn the author's notation, but once this barrier has been surmounted, it is clear sailing. The author also demonstrates a depth of knowledge of many areas of mathematics.