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Variational Regularization for Systems of Inverse Problems

Tikhonov Regularization with Multiple Forward Operators

  • Book
  • © 2019

Overview

Authors:
  1. Richard Huber

    1. Graz, Austria

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  • Rigorous analysis of systems of inverse problems

Part of the book series: BestMasters (BEST)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction

    • Richard Huber
    Pages 1-13

  3. General Tikhonov Regularisation

    • Richard Huber
    Pages 15-37

  4. Specific Discrepancies

    • Richard Huber
    Pages 39-61

  5. Regularisation Functionals

    • Richard Huber
    Pages 63-88

  6. Application to STEM Tomography Reconstruction

    • Richard Huber
    Pages 89-127

  7. Back Matter

    Pages 129-136
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Keywords

About this book

Tikhonov regularization is a cornerstone technique in solving inverse problems with applications in countless scientific fields. Richard Huber discusses a multi-parameter Tikhonov approach for systems of inverse problems in order to take advantage of their specific structure. Such an approach allows to choose the regularization weights of each subproblem individually with respect to the corresponding noise levels and degrees of ill-posedness.


Authors and Affiliations

  • Graz, Austria

    Richard Huber

About the author

Richard Huber wrote his master’s thesis under the supervision of Prof. Dr. Kristian Bredies at the Institute for Mathematics and Scientific Computing at Graz University, Austria.

Bibliographic Information

  • Book Title: Variational Regularization for Systems of Inverse Problems

  • Book Subtitle: Tikhonov Regularization with Multiple Forward Operators

  • Authors: Richard Huber

  • Series Title: BestMasters

  • DOI: https://doi.org/10.1007/978-3-658-25390-5

  • Publisher: Springer Spektrum Wiesbaden

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2019

  • Softcover ISBN: 978-3-658-25389-9Published: 27 February 2019

  • eBook ISBN: 978-3-658-25390-5Published: 14 February 2019

  • Series ISSN: 2625-3577

  • Series E-ISSN: 2625-3615

  • Edition Number: 1

  • Number of Pages: IX, 136

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Applications of Mathematics, Analysis, Computational Mathematics and Numerical Analysis

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