Mathematical Modeling in Biomedical Imaging I: Electrical and Ultrasound Tomographies, Anomaly Detection, and Brain Imaging (Lecture Notes in Mathematics, 1983)

This volume gives an introduction to a fascinating research area to applied mathematicians. It is devoted to providing the exposition of promising analytical and numerical techniques for solving challenging biomedical imaging problems, which trigger the investigation of interesting issues in various branches of mathematics. Front Matter....Pages 1-11 Multi-Frequency Electrical Impedance Tomography and Magnetic Resonance Electrical Impedance Tomography....Pages 1-71 Time Reversing Waves For Biomedical Applications....Pages 73-97 The Method of Small-Volume Expansions for Medical Imaging....Pages 99-132 Electric and Magnetic Activity of the Brain in Spherical and Ellipsoidal Geometry....Pages 133-202 Estimation of Velocity Fields and Propagation on Non-Euclidian Domains: Application to the Exploration of Cortical Spatiotemporal Dynamics....Pages 203-226 Back Matter....Pages 1-8 Multi-frequency Electrical Impedance Tomography And Magnetic Resonance Electrical Impedance Tomography -- Time Reversing Waves In Biomedical Applications -- The Method Of Small-volume Expansions For Medical Imaging -- Electric And Magnetic Activity Of The Brain In Spherical And Ellipsoidal Geometry -- Estimation Of Velocity Fields And Propagation On Non-euclidean Domains: Application To The Exploration Of Cortical Spatiotemporal Dynamics. Habib Ammari (ed.). Includes Bibliographical References And Index. This volume details promising analytical and numerical techniques for solving challenging biomedical imaging problems, which trigger the investigation of interesting issues in various branches of mathematics.