Preface 
List of important symbols

1 Introduction

1.1. Tomography 
1.2. Fields of application 
1.3. Complex systems

2. Numerical problem analysis
2.1. Formulation of the problem 
2.2. Forward problem 
2.3. Formulating the inverse problem 
2.4. Objective function 
2.5. Sensitivity analysis 

3. Tomographic methods 
3.1. Genesis and types of tomography 
3.2. Electrical tomography 
3.3. Electrical impedance/resistance tomography
3.4. Electrical capacitance tomography 
3.5. Ultrasound transmission tomography
3.6. Radio tomography 

4. Algorithms and image reconstructions 
4.1. Methods of image reconstruction 
4.2. Deterministic method 
4.2.1. Gauss-Newton method
4.2.2. Linear Back Projection 
4.2.3. Landweber algorithm 
4.2.4. Levenberg iterative method 
4.2.5. D-bar method
4.2.6. Implementations of modified algorithms 
4.2.7. Transmission tomography and mathematical methods
in image reconstruction
4.2.8. SVD method for solving overdetermined linear equations 
4.2.9. Development of the RayIntegration method 
4.2.10. Application of the Fresnel zone and Free-space Path Loss
4.3. Topological algorithms
4.3.1. Material derivative 
4.3.2. Shape derivative 
4.3.3. Topological derivative
4.3.4. Level set method
4.3.5. 3D Level set method 
4.3.6. Hybrid techniques to solve optimization problems 
4.3.7. Coupled LSM with BEM 
4.4. Machine learning 
4.4.1. Methods - introduction 
4.4.2. Problem definition 
4.4.3. PCR and PLSR
4.4.4. Elastic net 
4.4.5. Least Angle Regression algorithm 
4.4.6. Support Vector Machine 
4.4.7. Support Vector Machine for Regression 
4.4.8. Support Vector Machine for Regression with a modified
correlation kernel 
4.4.9. Logistic regression in image reconstruction 
4.4.10. Multiply Neural Networks
4.4.11. Tomographic imaging with Deep Learning 

5. Applications 
5.1. Distributed systems
5.2. Monitoring system of flood embankments 
5.2.1. Idea 
5.2.2. Description of the problem 
5.2.3. Materials and Methods 
5.2.4. Models of a Flood Embankment 
5.2.5. Laboratory models 
5.2.6. EIT device 
5.2.7. Active Electrode
5.2.8. ERT solution 
5.2.9. Hybrid electrical measurements device 
5.2.10. 2D image reconstruction
5.2.11. 3D image reconstruction 
5.2.12. Multisensor electrodes
5.2.13. Machine learning – Elastic net method 
5.2.14. Discussion and conclusion 
5.3. Detection of moisture walls and historical buildings 
5.3.1. Problem description 
5.3.2. Materials and Methods 
5.3.3. Model of a brick 
5.3.4. Brick cube
5.3.5. Airbrick 
5.3.6. Models of Walls 
5.3.7. Hybrid tomography scanner 1A 
5.3.8. 2D image reconstruction 
5.3.9. 3D image reconstruction
5.3.10. Comparison of image reconstruction 
5.3.11. Discussion and conclusion 
5.4. Industrial tomography 
5.4.1. Industrial tomography system
5.4.2. Materials and Methods 
5.4.3. Hybrid tomography scanner 1B 
5.4.4. Ultrasound tomography solution 
5.4.5. Wire mesh sensor 
5.4.6. Smart ECT 
5.4.7. Measurements and reconstructions by UTT
5.4.8. ECT image reconstruction 
5.4.9. Neural reconstruction for tomographic images 
5.4.10. Image reconstruction for small objects
5.4.11. Comparison of methods 
5.4.12. Technological challenges and summary 
5.5. Medical applications
5.5.1. System idea 
5.5.2. Hardware solution 
5.5.3. Image reconstruction 
5.5.4. Numerical model based on the human model
5.5.5. Discussion and summary 
5.6. Location system 
5.6.1. Idea 
5.6.2. Hardware and measurements 
5.6.3. Image reconstruction 
5.6.4. Summary 

6. Summary and conclusion 
Bibliography
 

• Title: Tomographic imaging in environmental, industrial and medical applications
• Author: Tomasz Rymarczyk
• ISBN: 978-83-66159-11-2, 9788366159112
• Date of issue: 2023-01-16
• Format: Ebook
• Item ID: e_30yd
• Publisher: Lubelska Akademia WSEI