Reconstruction from integral 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 fr...
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| Format: | eBook |
| Language: | English |
| Published: |
Boca Raton :
Chapman and Hall/CRC,
2016.
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| Edition: | 1st. |
| Series: | Monographs and research notes in mathematics.
Online access with DDA: Askews (Maths) |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| Summary: | 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. |
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| Physical Description: | 1 online resource : illustrations (black and white). |
| ISBN: | 9781498710114 1498710115 1498710107 9781498710107 |