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Reconstruction from Integral Data.
・ISBN 978-1-4987-1010-7 hard GB£ 187.99
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電子版あり 大学・学術機関向け電子ブック（eBook）ISBN 978-0-429-18317-1
| 著者・編者 | Palamodov, Victor, |
|---|---|
| シリーズ | Chapman & Hall/CRC Monographs and Research Notes in Mathematics |
| 出版社 | (Chapman & Hall/CRC, US) |
| 出版年月 | 2016 |
| ページ数 | 172 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-7084 M25-9850＞ |
解説
Reconstruction of a function from data of integrals is used for problems arising in diagnostics, including x-ray, positron radiography, ultrasound, scattering, sonar, seismic, impedance, wave tomography, crystallography, photo-thermo-acoustics, photoelastics, and strain tomography.
Reconstruction from Integral Data presents both long-standing and recent mathematical results from this field in a uniform way. The book focuses on exact analytic formulas for reconstructing a function or a vector field from data of integrals over lines, rays, circles, arcs, parabolas, hyperbolas, planes, hyperplanes, spheres, and paraboloids. It also addresses range characterizations. Coverage is motivated by both applications and pure mathematics.
The book first presents known facts on the classical and attenuated Radon transform. It then deals with reconstructions from data of ray (circle) integrals. The author goes on to cover reconstructions in classical and new geometries. The final chapter collects necessary definitions and elementary facts from geometry and analysis that are not always included in textbooks.