The Method of Approximate Inverse: Theory and Applications

  • Thomas┬áSchuster

Part of the Lecture Notes in Mathematics book series (LNM, volume 1906)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Inverse and Semi-discrete Problems

    1. Front Matter
      Pages 1-4
    2. Thomas Schuster
      Pages 11-24
    3. Thomas Schuster
      Pages 25-38
    4. Thomas Schuster
      Pages 39-47
    5. Thomas Schuster
      Pages 49-49
  3. Application to 3D Doppler Tomography

    1. Front Matter
      Pages 51-54
    2. Thomas Schuster
      Pages 55-61
    3. Thomas Schuster
      Pages 63-79
    4. Thomas Schuster
      Pages 81-87
    5. Thomas Schuster
      Pages 89-103
    6. Thomas Schuster
      Pages 105-106
  4. Application to the spherical mean operator

    1. Front Matter
      Pages 107-110
    2. Thomas Schuster
      Pages 111-121
    3. Thomas Schuster
      Pages 123-131
    4. Thomas Schuster
      Pages 133-137
    5. Thomas Schuster
      Pages 139-144
    6. Thomas Schuster
      Pages 145-145
  5. Further Applications

    1. Front Matter
      Pages 147-149

About this book

Introduction

Inverse problems arise whenever one tries to calculate a required quantity from given measurements of a second quantity that is associated to the first one. Besides medical imaging and non-destructive testing, inverse problems also play an increasing role in other disciplines such as industrial and financial mathematics. Hence, there is a need for stable and efficient solvers. The book is concerned with the method of approximate inverse which is a regularization technique for stably solving inverse problems in various settings such as L2-spaces, Hilbert spaces or spaces of distributions.  The performance and functionality of the method is demonstrated on several examples from medical imaging and non-destructive testing such as computerized tomography, Doppler tomography, SONAR, X-ray diffractometry and thermoacoustic computerized tomography. The book addresses graduate students and researchers interested in the numerical analysis of inverse problems and regularization techniques or in efficient solvers for the applications mentioned above.

Keywords

Doppler tomography Inverse problem approximate inverse numerical analysis reconstruction kernel regularization method

Authors and affiliations

  • Thomas┬áSchuster
    • 1
  1. 1.Department of Mechanical EngineeringHelmut Schmidt UniversityHamburgGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-71227-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2007
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-71226-8
  • Online ISBN 978-3-540-71227-5
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book