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Electrical impedance tomography: a fair comparative study on deep learning and analytic-based approaches

  • Derick Nganyu Tanyu , Jianfeng Ning , Andreas Hauptmann , Bangti Jin and Peter Maass
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Data-driven Models in Inverse Problems
This chapter is in the book Data-driven Models in Inverse Problems

Abstract

Electrical impedance tomography (EIT) is a powerful imaging technique with diverse applications, e. g., medical diagnosis, industrial monitoring, and environmental studies. The EIT inverse problem is about inferring the internal conductivity distribution of an object from measurements taken on its boundary. It is severely ill-posed, necessitating advanced computational methods for accurate image reconstructions. Recent years have witnessed significant progress, driven by innovations in analytic-based approaches and deep learning. This review comprehensively explores techniques for solving the EIT inverse problem, focusing on the interplay between contemporary deep learning-based strategies and classical analytic-based methods. Four state of the art deep learning algorithms are rigorously examined, including the deep D-bar method, deep direct sampling method, fully connected U-net, and convolutional neural networks, harnessing the representational capabilities of deep neural networks to reconstruct intricate conductivity distributions. In parallel, two analytic-based methods, i. e., sparsity regularization and the D-bar method, rooted in mathematical formulations and regularization techniques, are dissected for their strengths and limitations. These methodologies are evaluated through an extensive array of numerical experiments, encompassing diverse scenarios that reflect real-world complexities. A suite of performance metrics is employed to assess the efficacy of these methods. These metrics collectively provide a nuanced understanding of the methods’ ability to capture essential features and delineate complex conductivity patterns. One novel feature of the study is the incorporation of variable conductivity scenarios, introducing a level of heterogeneity that mimics textured inclusions. This departure from uniform conductivity assumptions mimics realistic scenarios, where tissues or materials exhibit spatially varying electrical properties. Exploring how each method responds to such variable conductivity scenarios opens avenues for understanding their robustness and adaptability.

Abstract

Electrical impedance tomography (EIT) is a powerful imaging technique with diverse applications, e. g., medical diagnosis, industrial monitoring, and environmental studies. The EIT inverse problem is about inferring the internal conductivity distribution of an object from measurements taken on its boundary. It is severely ill-posed, necessitating advanced computational methods for accurate image reconstructions. Recent years have witnessed significant progress, driven by innovations in analytic-based approaches and deep learning. This review comprehensively explores techniques for solving the EIT inverse problem, focusing on the interplay between contemporary deep learning-based strategies and classical analytic-based methods. Four state of the art deep learning algorithms are rigorously examined, including the deep D-bar method, deep direct sampling method, fully connected U-net, and convolutional neural networks, harnessing the representational capabilities of deep neural networks to reconstruct intricate conductivity distributions. In parallel, two analytic-based methods, i. e., sparsity regularization and the D-bar method, rooted in mathematical formulations and regularization techniques, are dissected for their strengths and limitations. These methodologies are evaluated through an extensive array of numerical experiments, encompassing diverse scenarios that reflect real-world complexities. A suite of performance metrics is employed to assess the efficacy of these methods. These metrics collectively provide a nuanced understanding of the methods’ ability to capture essential features and delineate complex conductivity patterns. One novel feature of the study is the incorporation of variable conductivity scenarios, introducing a level of heterogeneity that mimics textured inclusions. This departure from uniform conductivity assumptions mimics realistic scenarios, where tissues or materials exhibit spatially varying electrical properties. Exploring how each method responds to such variable conductivity scenarios opens avenues for understanding their robustness and adaptability.

Chapters in this book

  1. Frontmatter I
  2. Preface V
  3. Contents VII
  4. Part I: Mathematical aspects of data-driven methods in inverse problems
  5. On optimal regularization parameters via bilevel learning 1
  6. Learned regularization for inverse problems 39
  7. Inverse problems with learned forward operators 73
  8. Unsupervised approaches based on optimal transport and convex analysis for inverse problems in imaging 107
  9. Learned reconstruction methods for inverse problems: sample error estimates 163
  10. Statistical inverse learning problems with random observations 201
  11. General regularization in covariate shift adaptation 245
  12. Part II: Applications of data-driven methods in inverse problems
  13. Analysis of generalized iteratively regularized Landweber iterations driven by data 273
  14. Integration of model- and learning-based methods in image restoration 303
  15. Dynamic computerized tomography using inexact models and motion estimation 331
  16. Deep Bayesian inversion 359
  17. Utilizing uncertainty quantification variational autoencoders in inverse problems with applications in photoacoustic tomography 413
  18. Electrical impedance tomography: a fair comparative study on deep learning and analytic-based approaches 437
  19. Classification with neural networks with quadratic decision functions 471
  20. Index 495
https://doi.org/10.1515/9783111251233-013

Chapters in this book

  1. Frontmatter I
  2. Preface V
  3. Contents VII
  4. Part I: Mathematical aspects of data-driven methods in inverse problems
  5. On optimal regularization parameters via bilevel learning 1
  6. Learned regularization for inverse problems 39
  7. Inverse problems with learned forward operators 73
  8. Unsupervised approaches based on optimal transport and convex analysis for inverse problems in imaging 107
  9. Learned reconstruction methods for inverse problems: sample error estimates 163
  10. Statistical inverse learning problems with random observations 201
  11. General regularization in covariate shift adaptation 245
  12. Part II: Applications of data-driven methods in inverse problems
  13. Analysis of generalized iteratively regularized Landweber iterations driven by data 273
  14. Integration of model- and learning-based methods in image restoration 303
  15. Dynamic computerized tomography using inexact models and motion estimation 331
  16. Deep Bayesian inversion 359
  17. Utilizing uncertainty quantification variational autoencoders in inverse problems with applications in photoacoustic tomography 413
  18. Electrical impedance tomography: a fair comparative study on deep learning and analytic-based approaches 437
  19. Classification with neural networks with quadratic decision functions 471
  20. Index 495
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