Geometric Inverse Problems (Hardcover) (ISBN-13: 9781316510872)

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 Calder 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.

Author: Gabriel P. Paternain, Mikko Salo, Gunther Uhlmann
ISBN-10: 1316510875
ISBN-13: 9781316510872
Publisher: Cambridge University Press
Language: English
Published: 01/05/2023
Pages: 350
Format: Hardcover
Weight: 1.57lbs
Size: 9.00h x 6.00w x 0.94d