Reconstruction from integral data
- Victor Palamodov.
- Boca Raton, FL : CRC Press Taylor & Francis Group, 
- Copyright notice
- Physical description
- 169 pages : illustrations ; 24 cm.
- Monographs and research notes in mathematics.
At the library
Science Library (Li and Ma)
|QA477 .P35 2016||Unknown|
- Palamodov, V. P. (Viktor Pavlovich), author.
- Includes bibliographical references (pages 153-163) and index.
- Radon Transform Radon Transform and Inversion Range Conditions and Frequency Analysis Support Theorem Reconstruction of Functions from Attenuated Integrals Reconstruction of Differential Forms
- Ray and Line Integral Transforms Introduction Reconstruction from Line Integrals Range Conditions Shift-Invariant FBP Reconstruction Backprojection Filtration Method Tuy's Regularized Method Ray Integrals of Differential Forms Symmetric Tensors and Differentials Reconstruction from Ray Integrals
- Factorization Method Factorable Maps Spaces of Constant Curvature Funk Transform on the Orthogonal Group Reconstruction from Non-Redundant Data Range Conditions
- General Method of Reconstruction Geometric Integral Transforms Reconstruction Integral Transforms with Weights Resolved Generating Functions Analysis of Convergence Wave Front of Integral Transform
- Applications to Classical Geometries Minkowski-Funk Transform Nongeodesic Hyperplane Sections of a Sphere Totally Geodesic Transform in Hyperbolic Spaces Horospherical Transform Hyperboloids Cormack's Curves Confocal Paraboloids Cassini Ovals and Ovaloids
- Applications to the Spherical Mean Transform Oscillatory Sets Reconstruction Examples Time Reversal Structure Boundary Isometry for Waves in a Cavity Range Conditions Spheres Tangent to a Hyperplane Summary of Spherical Mean Transform
- Bibliographic notes appear at the end of each chapter.
- (source: Nielsen Book Data)
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.
(source: Nielsen Book Data)
- Publication date
- Copyright date
- Monographs and Research Notes in Mathematics
- "A Chapman & Hall book."
- 9781498710107 (hbk.)
- 1498710107 (hbk.)
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