The Mathematics of Computerized Tomography (Classics in Applied Mathematics) [Paperback]

Frank Natterer (Author)

Book Description

ISBN-10: 0898714931 | ISBN-13: 978-0898714937 | Publication Date: July 2001

This book provides a unified view of tomographic techniques, a common mathematical framework, and an in-depth treatment of reconstruction algorithms. It focuses on the reconstruction of a function from line or plane integrals, with special emphasis on applications in radiology, science, and engineering. The Mathematics of Computerized Tomography covers the relevant mathematical theory of the Radon transform and related transforms and also studies more practical questions such as stability, sampling, resolution, and accuracy. Quite a bit of attention is given to the derivation, analysis, and practical examination of reconstruction algorithms, for both standard problems and problems with incomplete data.

Editorial Reviews

Book Description

This book provides a unified view of tomographic techniques, a common mathematical framework, and an in-depth treatment of reconstruction algorithms. It focuses on the reconstruction of a function from line or plane integrals, with special emphasis on applications in radiology, science, and engineering.

From the Publisher

Details the reconstruction of a function from line or plane integrals, with special emphasis on applications in science, radiology and engineering. Both the relevant mathematical theory of the Radon transform and related transforms, and practical questions such as sampling, resolution, stability, and accuracy, are covered. Much space is given to the derivation, analysis and practical examination of reconstruction algorithms, both for standard problems and problems with incomplete data. --This text refers to an out of print or unavailable edition of this title.

See all Editorial Reviews

Product Details

• Paperback: 222 pages
• Publisher: SIAM: Society for Industrial and Applied Mathematics (July 2001)
• Language: English
• ISBN-10: 0898714931
• ISBN-13: 978-0898714937
• Product Dimensions: 9.2 x 6.1 x 0.5 inches
• Shipping Weight: 12 ounces (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #1,377,970 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

12 of 12 people found the following review helpful:

5.0 out of 5 stars A must read for students of the Radon transform, May 28, 2000

By A Customer

This review is from: The Mathematics of Computerized Tomography (Hardcover)

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.