Reconstruction from Integral Data

ISBN-13: 9781498710107 / Angielski / Twarda / 2016 / 172 str.

Victor Palamodov

Opis

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.

Spis treści

Radon Transform. Ray and Line Integral Transforms. Factorization Method. General Method of Reconstruction. Applications to Classical Geometries. Applications to the Spherical Mean Transform. Appendix.

O autorze

Victor Palamodov is a professor in the School of Mathematical Sciences at Tel-Aviv University. His research interests include mathematical and algebraic analysis and applications to physics and medical diagnostics.