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Deep Learning Methods for Limited Data Problems in X-Ray Tomography

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Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

Abstract

Successful medical diagnosis heavily relies on the reconstruction and analysis of images showing organs, bones, and other structures in the interior of the human body. In the last couple of years, the stored image data has increased tremendously, and also the computing power of modern GPUs experienced huge progress. Machine learning methods, and in particular deep learning methods, are on the rise to tackle advanced image reconstruction and image analysis tasks to support medical doctors in their diagnostic routines. In this chapter, we focus on the reconstruction task; especially consider tomographic imaging problems with incomplete, corrupted, or noisy data; and demonstrate how deep learning methods enable us to solve such tasks in a unified manner. We present the basic ideas of these methods assuming paired training data (supervised learning) and utilizing only feed-forward networks. In particular, we illustrate the underlying concepts for missing data problems in classical computed tomography (CT), noting that most of the concepts can be transferred to other inverse imaging problems.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Innsbruck, Innsbruck, Austria

    Johannes Schwab

Authors
  1. Johannes Schwab
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Corresponding author

Correspondence to Johannes Schwab .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, The University of Liverpool, Liverpool, UK

    Ke Chen

  2. Dept Appl Math & Theoretical Phys, University of Cambridge, Cambridge, UK

    Carola-Bibiane Schönlieb

  3. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong

    Xue-Cheng Tai

  4. Department of Applied Mathematics & Stat, Johns Hopkins University, Baltimore, MD, USA

    Laurent Younces

Section Editor information

  1. Department of Mathematical Sciences, University of Liverpool Mathematical Sciences Building, Liverpool, UK

    Ke Chen Ph.D

  2. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China

    Xuecheng Tai Ph.D

  3. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK

    Carola Schönlieb Ph.D

  4. Department of Applied Mathematics and Statistics, The Johns Hopkins University, Baltimore, MD, USA

    Laurent Younes

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Schwab, J. (2022). Deep Learning Methods for Limited Data Problems in X-Ray Tomography. In: Chen, K., Schönlieb, CB., Tai, XC., Younces, L. (eds) Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging. Springer, Cham. https://doi.org/10.1007/978-3-030-03009-4_82-1

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  • DOI: https://doi.org/10.1007/978-3-030-03009-4_82-1

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  • Print ISBN: 978-3-030-03009-4

  • Online ISBN: 978-3-030-03009-4

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