Geometric Inverse Problems : With Emphasis on Two Dimensions PDF
by Gabriel P. (University of Cambridge) Paternain, Mikko (University of Jyvaskyla, Finland) Salo, Gunther (University of Washington) Uhlmann
Part of the Cambridge Studies in Advanced Mathematics series
Description
This up-to-date treatment of recent developments in geometric inverse problems introduces graduate students and researchers to an exciting area of research.
With an emphasis on the two-dimensional case, topics covered include geodesic X-ray transforms, boundary rigidity, tensor tomography, attenuated X-ray transforms and the Calderón problem.
The presentation is self-contained and begins with the Radon transform and radial sound speeds as motivating examples.
The required geometric background is developed in detail in the context of simple manifolds with boundary.
An in-depth analysis of various geodesic X-ray transforms is carried out together with related uniqueness, stability, reconstruction and range characterization results.
Highlights include a proof of boundary rigidity for simple surfaces as well as scattering rigidity for connections.
The concluding chapter discusses current open problems and related topics.
The numerous exercises and examples make this book an excellent self-study resource or text for a one-semester course or seminar.
Information
-
Download - Immediately Available
- Format:PDF
- Pages:Worked examples or Exercises
- Publisher:Cambridge University Press
- Publication Date:21/12/2022
- Category:
- ISBN:9781009041423
Information
-
Download - Immediately Available
- Format:PDF
- Pages:Worked examples or Exercises
- Publisher:Cambridge University Press
- Publication Date:21/12/2022
- Category:
- ISBN:9781009041423
