Table of Contents
1.3 Issues in Inverse Problem Solving
1.4 Linear, Nonlinear and Linearized Problems
Chapter 2: Signal and System as Vectors
2.4 Linear System of Equations
Chapter 3: Basics of Forward Problem
3.1 Understanding a PDE using Images as Examples
3.4 Laplace and Poisson Equations
Chapter 4: Analysis for Inverse Problem
4.1 Examples of Inverse Problems in Medical Imaging
4.4 Tikhonov Regularization and Spectral Analysis
5.1 Iterative Method for Nonlinear Problem
5.2 Numerical Computation of One-Dimensional Heat Equation
5.3 Numerical Solution of Linear System of Equations
5.4 Finite Difference Method (FDM)
5.5 Finite Element Method (FEM)
Chapter 6: CT, MRI and Image Processing Problems
6.2 Magnetic Resonance Imaging
Chapter 7: Electrical Impedance Tomography
7.2 Measurement Method and Data
7.3 Representation of Physical Phenomena
7.5 Uniqueness Theory and Direct Reconstruction Method
7.7 Sensitivity and Sensitivity Matrix
7.11 Frequency-Difference Imaging
Chapter 8: Anomaly Estimation and Layer Potential Techniques
8.1 Harmonic Analysis and Potential Theory
8.2 Anomaly Estimation using EIT
8.3 Anomaly Estimation using Planar Probe
Chapter 9: Magnetic Resonance Electrical Impedance Tomography
9.2 Forward Problem and Model Construction
9.3 Inverse Problem Formulation using B or J
9.4 Inverse Problem Formulation using Bz
9.5 Image Reconstruction Algorithm
9.6 Validation and Interpretation
Chapter 10: Magnetic Resonance Elastography
10.1 Representation of Physical Phenomena
10.2 Forward Problem and Model