Variational Methods in Imaging

  • Otmar Scherzer
  • Markus Grasmair
  • Harald Grossauer
  • Markus Haltmeier
  • Frank Lenzen

Part of the Applied Mathematical Sciences book series (AMS, volume 167)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Fundamentals of Imaging

    1. Front Matter
      Pages 1-1
    2. Otmar Scherzer, Markus Grasmair, Harald Grossauer, Markus Haltmeier, Frank Lenzen
      Pages 3-25
    3. Otmar Scherzer, Markus Grasmair, Harald Grossauer, Markus Haltmeier, Frank Lenzen
      Pages 27-49
  3. Regularization

    1. Front Matter
      Pages 51-51
    2. Otmar Scherzer, Markus Grasmair, Harald Grossauer, Markus Haltmeier, Frank Lenzen
      Pages 53-113
    3. Otmar Scherzer, Markus Grasmair, Harald Grossauer, Markus Haltmeier, Frank Lenzen
      Pages 115-158
    4. Otmar Scherzer, Markus Grasmair, Harald Grossauer, Markus Haltmeier, Frank Lenzen
      Pages 159-183
    5. Otmar Scherzer, Markus Grasmair, Harald Grossauer, Markus Haltmeier, Frank Lenzen
      Pages 185-203
    6. Otmar Scherzer, Markus Grasmair, Harald Grossauer, Markus Haltmeier, Frank Lenzen
      Pages 205-218
  4. Mathematical Foundations

    1. Front Matter
      Pages 219-219
    2. Otmar Scherzer, Markus Grasmair, Harald Grossauer, Markus Haltmeier, Frank Lenzen
      Pages 221-238
    3. Otmar Scherzer, Markus Grasmair, Harald Grossauer, Markus Haltmeier, Frank Lenzen
      Pages 239-272
    4. Otmar Scherzer, Markus Grasmair, Harald Grossauer, Markus Haltmeier, Frank Lenzen
      Pages 273-286
  5. Back Matter
    Pages 287-320

About this book

Introduction

This book is devoted to the study of variational methods in imaging. The presentation is mathematically rigorous and covers a detailed treatment of the approach from an inverse problems point of view.

Key Features:

- Introduces variational methods with motivation from the deterministic, geometric, and stochastic point of view

- Bridges the gap between regularization theory in image analysis and in inverse problems

- Presents case examples in imaging to illustrate the use of variational methods e.g. denoising, thermoacoustics, computerized tomography

- Discusses link between non-convex calculus of variations, morphological analysis, and level set methods

- Analyses variational methods containing classical analysis of variational methods, modern analysis such as G-norm properties, and non-convex calculus of variations

- Uses numerical examples to enhance the theory

This book is geared towards graduate students and researchers in applied mathematics. It can serve as a main text for graduate courses in image processing and inverse problems or as a supplemental text for courses on regularization. Researchers and computer scientists in the area of imaging science will also find this book useful.

Keywords

Calculus of Variations acoustics image analysis image processing imaging science inverse problems regularization

Authors and affiliations

  • Otmar Scherzer
    • 1
  • Markus Grasmair
    • 1
  • Harald Grossauer
    • 1
  • Markus Haltmeier
    • 1
  • Frank Lenzen
    • 1
  1. 1.Department of MathematicsUniversity of Innsbruck6020 InsbruckAustria

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-69277-7
  • Copyright Information Springer Science+Business Media LLC 2009
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-30931-6
  • Online ISBN 978-0-387-69277-7
  • Series Print ISSN 0066-5452
  • About this book
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