Nonlinear Inverse Problems in Imaging

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Imaging techniques in science, engineering and medicine have evolved to expand our ability to visualize the electrical and mechanical properties of materials inside an object in the form of a cross-sectional image. There have been numerous research efforts to develop new techniques which produce additional contrast information unavailable from existing methods. This book discusses some of these latest imaging modalities: electrical impedance tomography (EIT), magnetic resonance electrical impedance tomography (MREIT) and magnetic resonance elastography (MRE). These imaging techniques all manifest some nonlinearity and this book focuses on their associated nonlinear inverse problems. The authors explain the mathematical and numerical tools needed to solve these problems in order to better visualize the electrical and mechanical properties inside a given object through these imaging techniques. Key features: * Provides an understanding of the underlying physical phenomena and implementation details of image reconstruction algorithms as prerequisites for finding solutions with practical significance and value. * Offers a self-contained treatment of the topic taking the reader from basic concepts, the mathematical background, computational methods and numerical simulations through to solved examples, practical limitations and case studies. * Describes forward problems and their mathematical formulations as they are often the processes of information loss and provide strategic insights in seeking solutions to nonlinear inverse problems. * Focuses on methods rather than applications. * Includes an accompanying website hosted by the authors containing lecture notes, computer programs and experimental data.