book

Nonlinear Inverse Problems in Imaging

December 2012

Intermediate to advanced

374 pages

10h 16m

English

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1.1 Forward Problem1.2 Inverse Problem1.3 Issues in Inverse Problem Solving1.4 Linear, Nonlinear and Linearized ProblemsReference
2.1 Vector Spaces2.2 Vector Calculus2.3 Taylor's Expansion2.4 Linear System of Equations2.5 Fourier TransformReferences
3.1 Understanding a PDE using Images as Examples3.2 Heat Equation3.3 Wave Equation3.4 Laplace and Poisson EquationsReferencesFurther Reading
4.1 Examples of Inverse Problems in Medical Imaging4.2 Basic Analysis4.3 Variational Problems4.4 Tikhonov Regularization and Spectral Analysis4.5 Basics of Real AnalysisReferencesFurther Reading
5.1 Iterative Method for Nonlinear Problem5.2 Numerical Computation of One-Dimensional Heat Equation5.3 Numerical Solution of Linear System of Equations5.4 Finite Difference Method (FDM)5.5 Finite Element Method (FEM)ReferencesFurther Reading

6.1 X-ray Computed Tomography6.2 Magnetic Resonance Imaging6.3 Image Restoration6.4 SegmentationReferencesFurther Reading
7.1 Introduction7.2 Measurement Method and Data7.3 Representation of Physical Phenomena7.4 Forward Problem and Model7.5 Uniqueness Theory and Direct Reconstruction Method7.6 Back-Projection Algorithm7.7 Sensitivity and Sensitivity Matrix7.8 Inverse Problem of EIT7.9 Static Imaging7.10 Time-Difference Imaging7.11 Frequency-Difference ImagingReferences
8.1 Harmonic Analysis and Potential Theory8.2 Anomaly Estimation using EIT8.3 Anomaly Estimation using Planar ProbeReferencesFurther Reading
9.1 Data Collection using MRI9.2 Forward Problem and Model Construction9.3 Inverse Problem Formulation using B or J9.4 Inverse Problem Formulation using Bz9.5 Image Reconstruction Algorithm9.6 Validation and Interpretation9.7 ApplicationsReferences
10.1 Representation of Physical Phenomena10.2 Forward Problem and Model10.3 Inverse Problem in MRE10.4 Reconstruction Algorithms10.5 Technical Issues in MREReferencesFurther Reading