Integral geometry and unique continuation principles

Abstract

This is the introductory part of my PhD thesis on inverse problems arising in medical and seismic imaging. The topics include X-ray tomography of scalar and vector fields with partial data, higher order fractional Calder\'on problems, travel time tomography on Riemannian and Finsler manifolds, and unique continuation of fractional Laplacians. The thesis additionally includes these articles: arXiv:1909.05585, arXiv:2001.06210, arXiv:2006.05790, arXiv:2008.10227, arXiv:2009.01043, arXiv:2010.11484, arXiv:2103.14385.