Nonlinear Inverse Problems in Imaging - Hardcover

Seo, Jin Keun; Woo, Eung Je

Hardcover

ISBN 10: 047066942X ISBN 13: 9780470669426

Publisher: Wiley, 2012

Synopsis

This book provides researchers and engineers in the imaging field with the skills they need to effectively deal with nonlinear inverse problems associated with different imaging modalities, including impedance imaging, optical tomography, elastography, and electrical source imaging. Focusing on numerically implementable methods, the book bridges the gap between theory and applications, helping readers tackle problems in applied mathematics and engineering. Complete, self-contained coverage includes basic concepts, models, computational methods, numerical simulations, examples, and case studies.

• Provides a step-by-step progressive treatment of topics for ease of understanding.
• Discusses the underlying physical phenomena as well as implementation details of image reconstruction algorithms as prerequisites for finding solutions to non linear inverse problems with practical significance and value.
• Includes end of chapter problems, case studies and examples with solutions throughout the book.
• Companion website will provide further examples and solutions, experimental data sets, open problems, teaching material such as PowerPoint slides and software including MATLAB m files.

Essential reading for Graduate students and researchers in imaging science working across the areas of applied mathematics, biomedical engineering, and electrical engineering and specifically those involved in nonlinear imaging techniques, impedance imaging, optical tomography, elastography, and electrical source imaging

About this title

About the Author

Jin Keun Seo, Department of Computational Science and Engineering, Yonsei University, Korea
Professor Seo is currently Chairman of the Computational Science and Engineering Department at Yonsei University, Korea. He has worked on a wide range of interdisciplinary areas including PDE, image processing, bio-impedance, mathematical modelling, harmonic analysis, and so on. He has published over 100 research papers in scientific journals including SIAM Journal on Applied Mathematics, Inverse Problems, IEEE Transactions on Medical Imaging, IEEE Transactions on Biomedical Engineering, Physics in Medicine and Biology, Physiological Measurement, and others. He has received distinguished research awards from the Korean Mathematical Society and Yonsei University. Since 2007, he has been an editor of Journal of Inverse Problems and Imaging.

Eung Je Woo, Department of Biomedical Engineering, Kyung Hee University, Korea
Professor Woo is currently with the Department of Biomedical Engineering, College of Electronics and Information, Kyung Hee University, Korea. Since 2002, he has been the director of Impedance Imaging Research Center (IIRC), Korea. For the past 20 years, he has been teaching undergraduate and graduate courses on medical instrumentation, biomedical computing, and impedance imaging. His research interests include biomedical instrumentation and imaging. From 2004 to 2010, he has been a co-organizer of international conferences on impedance imaging and electrical bioimpedance. In 2006, he served the scientific program chair of the World Congress on Medical Physics and Biomedical Engineering (WC2006). In 2009, he served the theme co-chair of IEEE EMBC09 for biomedical imaging and image processing.

From the Back Cover

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.

From the Inside Flap

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.

Edition details

• Publisher: Wiley
• Publication date: 2012
• Language: English
• ISBN 10: 047066942X
• ISBN 13: 9780470669426
• Binding: Hardcover
• Edition number: 1
• Number of pages: 374