Reconstruction from Integral Data (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)
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Reconstruction from Integral Data (Chapman & Hall/CRC Monograph...
Book Details:
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Author: Victor Palamodov
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Publisher: CRC Press
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Edition: 1st Edition
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Binding: Hardcover
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Number of Pages: 172
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Release Date: 02-05-2016
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EAN: 9781498710107
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Dimensions: 9.3 x 6.2 x 0.7 inches
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Language: English
About The Book:
Reconstruction from Integral Data explores the important concept of reconstructing a function from the data of integrals, a method crucial in various diagnostic fields such as X-ray, ultrasound, seismic, sonar, crystallography, photo-thermo-acoustics, and more. The book presents both traditional and recent mathematical advancements in the field, focusing on exact analytic formulas for reconstructing functions or vector fields from integrals over diverse geometric forms such as lines, rays, circles, spheres, parabolas, and planes.
The book's approach is motivated by both practical applications in fields like medical diagnostics and pure mathematical theory. It begins with a detailed discussion of the classical and attenuated Radon transform, before moving on to cover more advanced topics, including reconstructions from data of ray and circle integrals. It then transitions to discuss reconstructions in both classical and novel geometries.
The final chapter serves as a reference, providing definitions and elementary facts from geometry and analysis that are often left out of standard textbooks.
Key Features:
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Uniform presentation of both classical and recent results.
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Focus on reconstructions from a variety of integral data types.
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Practical applications in diagnostics such as X-ray, ultrasound, and tomography.
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Mathematical treatment suitable for both applied and theoretical audiences.
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Final chapter offering foundational material in geometry and analysis.
This book is invaluable for professionals and students working in areas such as medical imaging, geophysics, and other fields that rely on reconstructing data from integrals over complex geometries.
