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Linear and Nonlinear Inverse Problems with Practical Applications

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 Product Description

by Jennifer Mueller and Samuli Siltanen


2012 / xiv + 351 pages / Softcover / ISBN 978-1-611972-33-7 / List Price $84.00 / SIAM Member Price $58.80 / Order Code CS10

Keywords: inverse problem, reconstruction, regularization, tomography, computation

Inverse Problems Book Page

Inverse problems arise in practical applications whenever there is a need to interpret indirect measurements. This book

  • explains how to identify ill-posed inverse problems arising in practice and how to design computational solution methods for them;
  • explains computational approaches in a hands-on fashion, with related codes available on a website;
  • serves as a convenient entry point to practical inversion. 

The guiding linear inversion examples are the problem of image deblurring, x-ray tomography, and backward parabolic problems, including heat transfer, and electrical impedance tomography is used as the guiding nonlinear inversion example.

The book's nonlinear material combines the analytic-geometric research tradition and the regularization-based school of thought in a fruitful manner, paving the way to new theorems and algorithms for nonlinear inverse problems. Furthermore, it is the only mathematical textbook with a thorough treatment of electrical impedance tomography, and these sections are suitable for beginning and experienced researchers in mathematics and engineering.

Linear and Nonlinear Inverse Problems with Practical Applications is well-suited for students in mathematics, engineering, physics, or computer science who wish to learn computational inversion (inverse problems). Professors will find that the exercises and project work topics make this a suitable textbook for advanced undergraduate and graduate courses on inverse problems. Researchers developing large-scale inversion methods for linear or nonlinear inverse problems, as well as engineers working in research and development departments at high-tech companies and in electrical impedance tomography, will also find this a valuable guide.

About the Authors
Jennifer L. Mueller is a Professor of Mathematics and Biomedical Engineering at Colorado State University in Fort Collins, Colorado. Prior to that she was an NSF Postdoctoral Fellow at Rensselaer Polytechnic Institute in Troy, New York, where she began working in electrical impedance imaging. Clinical applications are a strong motivating factor in her research in reconstruction algorithms for medical imaging. She has served as Vice Chair and Program Director for the SIAM Activity Group on Imaging Science.

Samuli Siltanen works as a Professor of Industrial Mathematics at the University of Helsinki, Finland, and is a senior scientist in the Centre of Excellence in Inverse Problems Research nominated by the Academy of Finland for the periods 2006–2011 and 2012–2017. He has also worked as a research and development scientist at medical imaging technology companies, including GE Healthcare, and is President of the Finnish Inverse Problems Society.

ISBN 9781611972337

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