This monograph aims to synthesize methods, measurement architectures, and algorithms that advance approaches to electrical and ultrasonic tomography, with a particular focus on artificial intelligence in image reconstruction and decision support. The work places these techniques in modern, complex environmental, industrial, and medical diagnostic systems, where non-invasive measurements are required for reliable observation, control, and process optimization. The scope of this work encompasses forward and inverse problems, numerical modelling, and data-driven learning methods, and is based on practical prototypes and verified applications.

Tomographic imaging is presented as a family of techniques that infer internal structure based on boundary or remote measurements, enabling inspection without physical intervention. The theoretical foundations are outlined along with historical context and standard formulations of inverse problems, which are ill-posed and sensitive to noise and modelling errors. Established numerical frameworks, such as the Finite Element Method, are used to regularize and solve forward and inverse problems for electric and acoustic fields. These pillars provide a coherent path from physics to computation, and ultimately to images interpreted in an operational context. Artificial intelligence methods were applied to improve reconstruction fidelity, noise immunity, and computational efficiency. The text discusses deterministic frameworks such as Tikhonov, Gauss-Newton, and Total Variation, followed by a discussion of machine learning and deep learning architectures such as LSTM and CNN, along with ResNet, DiffNet, and specifically developed differential models for tomographic signals. The proposed multi-branch and pixel-centric strategies were evaluated using quantitative metrics such as RMSE, SSIM, ICC, Pearson correlation, relative image error, MAE, MAPE, and related metrics that reflect both perceptual and task-specific quality. The combination of physics-based modeling and prior knowledge has been shown to reduce inference time and increase noise tolerance compared to classical iterative solvers.

A significant portion of the monograph is devoted to the design and evolution of measurement devices. Electrical and hybrid tomographs, next-generation ultrasound tomographs, a beamforming platform, and specialized flaw detection solutions are designed and characterized. Portable and mobile configurations, along with body potential mapping, are used to extend tomographic detection capabilities to include outpatient and situational monitoring. The measurement layer is integrated with distributed acquisition, synchronization, and embedded processing, allowing the systems to operate within industrial and clinical constraints.

Applications in process engineering and medicine are presented. Fermentation control, crystallization monitoring, and autonomous process supervision illustrate industrial utility, including connections to the Internet of Things and real-time data infrastructure. Medical research includes non-invasive lung monitoring, portable diagnostics, and ultrasound brain detection, as well as portable hybrid ultrasound impedance solutions for lower urinary tract assessment. Non-destructive testing is addressed using advanced ultrasound imaging on the DefectoVision platform, which describes 3D reconstruction and quantitative assessment. These cases demonstrate that tomographic sensing can reveal internal states, detect anomalies, and support inspection without disrupting production or compromising safety.

The book is designed to guide the reader from fundamentals to implementations and verified use cases. Chapter 1 introduces tomographic imaging, the physical principles underlying electrical and ultrasound techniques, and the challenges of the inverse problem. Chapter 2 discusses reconstruction methods, from deterministic regularization to machine learning and deep learning, along with evaluation metrics. Chapter 3 documents the designed measurement devices along with their electronics, sensor geometry, and system characteristics. Chapter 4 develops reconstruction processes based on simulated and experimental datasets and discusses comparative performance, including hybrid and 3D approaches. Chapter 5 consolidates applications in industrial processes and medical diagnostics, presenting experimental setups, results, and discussions that link quantitative metrics to operational requirements. Chapter 6 concludes with a summary, conclusions, and perspectives for further development.

This publication is aimed at researchers and PhD students in the fields of sensors, inverse problems, and computational imaging, as well as engineers and practitioners responsible for process control, non-destructive testing, and medical technology assessment. The material was developed autonomously, with theoretical assumptions, numerical methods, device descriptions, and application studies, so that knowledge can be transferred from laboratory prototypes to real systems.

This work was developed thanks to the research community and collaboration at the Netrix S.A. Research and Development Centre and the Institute of Information Technology and Innovative Technologies at the WSEI University in Lublin. Appreciation is expressed to my colleagues who collaborated with me on research projects in the areas of device prototyping, data acquisition, and algorithm development, which translated concepts into working systems. We also extend our gratitude to the reviewers, whose insightful comments contributed to improved clarity and completeness, and to our family for their continued support.

The presented projects were developed to demonstrate how intelligent tomographic measurement systems can be constructed and deployed as reliable imaging, monitoring, and control tools. This synthesis of physics-based modelling and learning-based reasoning will be useful to both academia and industry seeking to implement practical, large-scale tomography.

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Spis treści

Artificial Intelligence in Electrical Tomography and Ultrasound Technologies Algorithms, Measurement Systems and Applications eBook -- spis treści

TABLE OF CONTENTS
Preface ............................................................................................................... 9
List of important symbols .............................................................................. 13
1. Introduction ............................................................................................... 17
1.1. Tomographic imaging .................................................................................... 17
1.2. Artificial Intelligence in Tomographic Inverse Problems .......................... 23
1.3. Electrical tomography .................................................................................... 25
1.3.1. Theoretical background........................................................................ 25
1.3.2. The forward and inverse problems in EIT.......................................... 26
1.3.3. Image reconstruction algorithm.......................................................... 28
1.4. Principles of ultrasound tomography .......................................................... 30
1.4.1. Physical fundamentals of transmission ultrasound imaging........... 30
1.4.2. Ultrasonic sensors................................................................................. 31
1.4.3. Algebraic tomographic imaging methods.......................................... 33
1.4.4. Image generation algorithm by changing the pixel shape................ 35
1.4.5. Definition of the objective function.................................................... 36
1.4.6. Theory of ultrasonic tomography........................................................ 37
1.5. Data acquisition in tomographic imaging techniques ............................... 47
1.5.1. Electrical impedance and resistance tomography............................. 47
1.5.2. Electrical capacitance tomography...................................................... 49
1.5.3. Ultrasound tomography solutions...................................................... 50
2. Image reconstruction methods .................................................................. 53
2.1. Methods of image reconstruction ................................................................ 53
2.2. Deterministic method .................................................................................... 55
2.2.1. Tikhonov Regularization...................................................................... 55
2.2.2. The Gauss-Newton Method................................................................. 56
2.2.3. Total Variation........................................................................................ 57
2.2.4. Kotre Method......................................................................................... 59
2.3. Machine learning ............................................................................................ 60
2.3.1. Introduction to machine learning methods....................................... 60
2.3.2. Elastic Net............................................................................................... 60
2.3.3. Least Angle Regression......................................................................... 61
2.3.4. Support Vector Machine....................................................................... 62
2.3.5. Regression methods.............................................................................. 63
2.3.6. Multiply Neural Networks.................................................................... 64
2.3.7. Method-oriented ensemble.................................................................. 65
2.4. Deep learning methods .................................................................................. 66
2.4.1. Long Short-Term Memory................................................................... 66
2.4.2. DL-Pixel Method................................................................................... 69
2.4.3. ResNet..................................................................................................... 70
2.4.4. DiffNet..................................................................................................... 72
2.5. Metrics ............................................................................................................. 73
2.5.1. Quantitative methods for model assessment..................................... 73
2.5.2. Root Mean Square Error ...................................................................... 73
2.5.3. Peak Signal-to-Noise Ratio................................................................... 74
2.5.4. Structural Similarity Index Measure................................................... 74
2.5.5. Intraclass Correlation Coefficient ....................................................... 75
2.5.6. Pearson Correlation Coefficient ......................................................... 76
2.5.7. Relative Image Error ............................................................................. 77
2.5.8. Mean Absolute Error ............................................................................ 77
2.5.9. Mean Absolute Percentage Error ........................................................ 78
2.5.10. Peak Error............................................................................................. 78
3. Measuring devices ...................................................................................... 81
3.1. Hybrid tomograph 1A .................................................................................... 81
3.2. Hybrid tomograph 1B .................................................................................... 84
3.3. SmartEIT .......................................................................................................... 87
3.4. Electrical tomograph 2.0 ................................................................................ 89
3.5. Electrical tomograph 2.1 ................................................................................ 97
3.6. Electrical tomograph 3.0 ................................................................................ 99
3.7. Ultrasound tomograph 1.0 .......................................................................... 104
3.8. Ultrasound tomograph 1.1 .......................................................................... 106
3.9. Ultrasound tomograph 2.0 .......................................................................... 109
3.10. Ultrasound tomograph 3.0 ........................................................................ 119
3.11. Ultrasound tomograph 4.0 ........................................................................ 126
3.12. Ultrasound Beamforming Tomograph .................................................... 131
3.13. Ultrasound defectoscope ........................................................................... 134
3.14. Device for diagnosis of functional disorders of the lower urinary
tract .............................................................................................................. 139
3.15. Electrical tomograph for innovative imaging and area monitoring .... 143
3.16. Mobile ultrasound-impedance tomograph ............................................ 152
4. Image reconstruction ............................................................................... 167
4.1. Reconstruction methods in electrical tomography .................................. 167
4.1.1. Introduction to reconstruction algorithms......................................167
4.1.2. Data preparation and simulation.......................................................167
4.1.3. Investigated reconstruction models..................................................169
4.1.4. Multi-branch Differential Neural Network .....................................173
4.1.5. Comparison of reconstructions based on simulation data............175
4.1.6. Experimental results and comparative analysis...............................185
4.1.7. Discussion.............................................................................................190
4.2. Reconstruction methods in ultrasound tomography .............................. 191
4.2.1. Numerical modelling and reconstruction methods........................191
4.2.2. Simulation environment.....................................................................192
4.2.3. Data preparation for the predictive model and network architecture....193
4.2.4. LSTM neural network ........................................................................197
4.2.5. CNN neural network...........................................................................200
4.2.6. Comparison of differential LSTM and differential CNN architectures.....203
4.2.7. Reconstructions with real data..........................................................205
4.2.8. Conclusions..........................................................................................207
4.3. Hybrid tomography ...................................................................................... 208
4.3.1. Image Analysis in process tomography............................................208
4.3.2. Reconstruction algorithms.................................................................208
4.3.3. Quantitative comparison of algorithms............................................230
4.3.4. A Hybrid EIT-UST System Implementation....................................232
4.3.5. Discussion of hybrid synergy.............................................................239
4.4. 3D Tomography ............................................................................................ 240
4.4.1. Network Architecture and Methodology.........................................240
4.4.2. Evaluation Metrics and Classifier Development.............................242
4.4.3. System optimizing of loss function...................................................244
4.4.4. Electrical tomography method for ECT and EIT............................250
5. Applications .............................................................................................. 261
5.1. Autonomous process control using electrical impedance tomography ....... 261
5.1.1. Introduction.........................................................................................261
5.1.2. Fermentation process..........................................................................263
5.1.3. Experimental setup..............................................................................263
5.1.4. Simulation environment.....................................................................266
5.1.5. Results...................................................................................................268
5.1.6. Discussion.............................................................................................270
5.2. Wearable Sensors for non-invasive monitoring and diagnosis .............. 272
5.2.1. Introduction.........................................................................................272
5.2.2. The proposed EIT solution and innovation.....................................272
5.2.3. System hardware and software design..............................................273
5.2.4. Machine learning applications for reconstruction..........................275
5.3. Tomographic system for imaging and area monitoring using body
potential mapping ....................................................................................... 282
5.3.1. Electrical tomography for medical diagnostics...............................282
5.3.2. Respiratory pathologies and existing diagnostics...........................283
5.3.3. System design.......................................................................................285
5.3.4. System performance and results........................................................290
5.3.5. Discussion.............................................................................................293
5.4. Non-invasive tomographic imaging for lung monitoring ....................... 294
5.4.1. Introduction.........................................................................................294
5.4.2. Methodology and experimental setup..............................................294
5.4.3. In-vivo sensor belt design...................................................................297
5.4.4. Image reconstruction..........................................................................302
5.5. Ultrasound tomography for brain sensing ................................................ 305
5.5.1. Introduction to USCT system............................................................305
5.5.2. Measurement and reconstruction methods.....................................306
5.5.3. Results and comparative analysis......................................................312
5.6. Advanced image reconstruction techniques in ultrasonic NDT ............ 315
5.6.1. DefectoVision 3D System...................................................................315
5.6.2. Data acquisition, processing, and algorithms..................................319
5.6.3. Performance evaluation and results..................................................322
5.6.4. Discussion.............................................................................................325
5.7. Tomographic system optimising technological processes ..................... 327
5.7.1. The use tomography in IoT systems..................................................327
5.7.2. Complex system...................................................................................327
5.7.3. Experimental results............................................................................330
5.7.4. Discussion and conclusion.................................................................335
5.8. Technological process tomography system ............................................... 336
5.8.1. Introduction.........................................................................................336
5.8.2. System design and architecture.........................................................337
5.8.3. System for crystallization process monitoring.................................344
5.8.4. Discussion.............................................................................................350
5.9. Portable ultrasonic-impedance tomograph for lower urinary
tract monitoring .......................................................................................... 351
5.9.1. Introduction.........................................................................................351
5.9.2. System hardware and design..............................................................352
5.9.3. Methodologies for image reconstruction.........................................353
5.9.4. Experimental validation and results.................................................358
5.9.5. Conclusion............................................................................................361
6. Summary and conclusion ......................................................................... 363
Bibliography ................................................................................................. 367