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
Table of Contents
- Title Page
- List of Abbreviations
- Chapter 1: Introduction
- Chapter 2: Signal and System as Vectors
- Chapter 3: Basics of Forward Problem
- Chapter 4: Analysis for Inverse Problem
- Chapter 5: Numerical Methods
- Chapter 6: CT, MRI and Image Processing Problems
Chapter 7: Electrical Impedance Tomography
- 7.1 Introduction
- 7.2 Measurement Method and Data
- 7.3 Representation of Physical Phenomena
- 7.4 Forward Problem and Model
- 7.5 Uniqueness Theory and Direct Reconstruction Method
- 7.6 Back-Projection Algorithm
- 7.7 Sensitivity and Sensitivity Matrix
- 7.8 Inverse Problem of EIT
- 7.9 Static Imaging
- 7.10 Time-Difference Imaging
- 7.11 Frequency-Difference Imaging
- Chapter 8: Anomaly Estimation and Layer Potential Techniques
- Chapter 9: Magnetic Resonance Electrical Impedance Tomography
- Chapter 10: Magnetic Resonance Elastography
- Title: Nonlinear Inverse Problems in Imaging
- Release date: December 2012
- Publisher(s): Wiley
- ISBN: 9781118478158