Monographs in Mathematics

Reconstructive Integral Geometry

Authors: Palamodov, Victor

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-0348-7941-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-3-7643-7129-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $99.00
price for USA
  • ISBN 978-3-0348-9629-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

Reviews

"This book is an excellent overview of the field of integral geometry with emphasis on the functional analytic and differential geometric aspects. The author proves theorems for some of the most important Radon transforms, including transforms on hyperplanes, k-planes, lines, and spheres, and he investigates incomplete (limited) data problems including microlocal analytic issues…This book contains many treasures in integral geometry…and it belongs on the shelf of any analyst or geometer who would like to see how deep functional analysis and differential geometry are used to solve important problems in integral geometry." —Mathematical Reviews


Table of contents (9 chapters)

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-0348-7941-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-3-7643-7129-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $99.00
price for USA
  • ISBN 978-3-0348-9629-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Reconstructive Integral Geometry
Authors
Series Title
Monographs in Mathematics
Series Volume
98
Copyright
2004
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-7941-5
DOI
10.1007/978-3-0348-7941-5
Hardcover ISBN
978-3-7643-7129-6
Softcover ISBN
978-3-0348-9629-0
Series ISSN
1017-0480
Edition Number
1
Number of Pages
XII, 164
Topics