One hundred years ago (1904) Hermann Minkowski [58] posed a problem: to re- 2 construct an even function I on the sphere 8 from knowledge of the integrals MI (C) = fc Ids over big circles C. Paul Funk found an explicit reconstruction formula for I from data of big circle integrals. Johann Radon studied a similar problem for the Eu- clidean plane and space. The interest in reconstruction problems like Minkowski- Funk's and Radon's has grown tremendously in the last four decades, stimulated by the spectrum of new modalities of image reconstruction. These are X-ray, MRI, gamma and positron radiography, ultrasound, seismic tomography, electron mi- croscopy, synthetic radar imaging and others. The physical principles of these methods are very different, however their mathematical models and solution meth- ods have very much in common. The umbrella name reconstructive integral geom- etryl is used to specify the variety of these problems and methods. The objective of this book is to present in a uniform way the scope of well- known and recent results and methods in the reconstructive integral geometry. We do not touch here the problems arising in adaptation of analytic methods to numerical reconstruction algorithms. We refer to the books [61], [62] which are focused on these problems. Various aspects of interplay of integral geometry and differential equations are discussed in Chapters 7 and 8. The results presented here are partially new.
| ISBN: | 9783764371296 |
| Publication date: | 1st August 2004 |
| Author: | V P Palamodov |
| Publisher: | Birkhauser an imprint of Birkhäuser Basel |
| Format: | Hardback |
| Pagination: | 164 pages |
| Series: | Monographs in Mathematics |
| Genres: |
Integral calculus and equations Functional analysis and transforms |
One hundred years ago (1904) Hermann Minkowski [58] posed a problem: to re- 2 construct an even function I on the sphere 8 from knowledge of the integrals MI (C) = fc Ids over big circles C. Paul Funk found an explicit reconstruction formula for I from data of big circle integrals. Johann Radon studied a similar problem for the Eu- clidean plane and space. The interest in reconstruction problems like Minkowski- Funk's and Radon's has grown tremendously in the last four decades, stimulated by the spectrum of new modalities of image reconstruction. These are X-ray, MRI, gamma and positron radiography, ultrasound, seismic tomography, electron mi- croscopy, synthetic radar imaging and others. The physical principles of these methods are very different, however their mathematical models and solution meth- ods have very much in common. The umbrella name reconstructive integral geom- etryl is used to specify the variety of these problems and methods. The objective of this book is to present in a uniform way the scope of well- known and recent results and methods in the reconstructive integral geometry. We do not touch here the problems arising in adaptation of analytic methods to numerical reconstruction algorithms. We refer to the books [61], [62] which are focused on these problems. Various aspects of interplay of integral geometry and differential equations are discussed in Chapters 7 and 8. The results presented here are partially new.
Reconstructive Integral Geometry features in the following genres: Integral calculus and equations, Functional analysis and transforms
Reconstructive Integral Geometry is available in Hardback
Reconstructive Integral Geometry was written by V P Palamodov and published by Birkhauser an imprint of Birkhäuser Basel
Reconstructive Integral Geometry has 164 pages
Yes it is part of Monographs in Mathematics series