Inverse problems lie at the heart of contemporary scientific inquiry and technological development. Applications include a variety of medical and other imaging techniques, which are used for early detection of cancer and pulmonary edema, location of oil and mineral deposits in the Earth's interior, creation of astrophysical images from telescope data, finding cracks and interfaces within materials, shape optimization, model identification in growth processes, and modeling in the life sciences among others. The expository survey essays in this book describe recent developments in inverse problems and imaging, including hybrid or couple-physics methods arising in medical imaging, Calderon's problem and electrical impedance tomography, inverse problems arising in global seismology and oil exploration, inverse spectral problems, and the study of asymptotically hyperbolic spaces. It is suitable for graduate students and researchers interested in inverse problems and their applications.
Dr Gunther Uhlmann is Walker Family Endowed Professor of Mathematics at the University of Washington, Department of Mathematics, and the Excellence in Teaching Endowed Chair at the University of California, Irvine. His research focuses on inverse problems and imaging, microlocal analysis and partial differential equations.
1. The Calderon's inverse problem: imaging and invisibility Kari Astala, Matti Lassas and Lassi Paivarinta; 2. Resistor network approaches to electrical impedance tomography Liliana Borcea, Vladimir Druskin, Fernando Guevara Vasquez and Alexander V. Mamonov; 3. Calderon inverse problem in two dimensions Colin Guillarmou and Leo Tzou; 4. The Calderon problem on Riemannian manifolds Mikko Salo; 5. Enclosure methods for the Helmholtz-type equations Jenn-Nan Wang and Ting Zhou; 6. Multiwave methods via ultrasound Plamen Stefanov and Gunther Uhlmann; 7. Hybrid inverse problems and internal functionals Guillaume Bal; 8. Inverse problems for connections Gabriel P. Paternain; 9. Elastic-wave inverse scattering based on reverse time migration with active and passive source reflection data Valeriy Brytik, Maarten V. de Hoop and Robert D. van der Hilst; 10. Inverse problems in spectral geometry Kiril Datchev and Hamid Hezari; 11. Microlocal analysis of asymptotically hyperbolic spaces and high energy resolvent estimates Andras Vasy; 12. Transmission eigenvalues in inverse scattering theory Fioralba Cakoni and Houssem Haddar.