C1 Book
Geometric Inverse Problems : With Emphasis on Two Dimensions (2023)

Paternain, G. P., Salo, M., & Uhlmann, G. (2023). Geometric Inverse Problems : With Emphasis on Two Dimensions. Cambridge University Press. Cambridge Studies in Advanced Mathematics, 204. https://doi.org/10.1017/9781009039901

JYU authors or editors

Publication details

All authors or editorsPaternain, Gabriel P.; Salo, Mikko; Uhlmann, Gunther



Journal or seriesCambridge Studies in Advanced Mathematics


Publication year2023

Publication date05/01/2023

Number in series204

Number of pages in the book344

PublisherCambridge University Press

Place of PublicationCambridge

Publication countryUnited Kingdom

Publication languageEnglish


Publication open accessNot open

Publication channel open access

Publication is parallel published (JYX)https://jyx.jyu.fi/handle/123456789/85367


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.

Keywordsmathematicsgeometryinverse problemstopologygeodesy

Free keywordsmathematics; abstract analysis; geometry and topology

Contributing organizations

Ministry reportingYes

Reporting Year2023

JUFO rating1

Last updated on 2024-02-07 at 23:27