Applied Mathematical Sciences

Variational Methods in Imaging

Authors: Scherzer, O., Grasmair, M., Grossauer, H., Haltmeier, M., Lenzen, F.

  • Introduces variational methods informed by the deterministic, geometric and stochastic point of view
  • Presents case examples in imaging to illustrate the use of variational methods e.g. denoising, thermoacoustics, and computerized tomography
  • Discusses the link between nonconvex 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 nonconvex calculus of variations
  • Includes additional material and images online
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eBook $59.99
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  • ISBN 978-0-387-69277-7
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  • Immediate eBook download after purchase
Hardcover $79.95
price for USA
  • ISBN 978-0-387-30931-6
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  • Usually dispatched within 3 to 5 business days.
Softcover $79.95
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  • ISBN 978-1-4419-2166-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

Reviews

From the reviews:

"Imaging is a wide area of applied mathematics which covers inverse problems, data filtering … medical diagnosis, etc. … The book is structured in a logical manner, starting with motivating examples and building on them. … One of the strengths of this book is its real-life applications and analytical and numerical results presented at each step, keeping the content real … . This is … a book for the seasoned researchers or graduate students who look to deepen their understanding of the subject." (Bogdan G. Nita, Mathematical Reviews, Issue 2009 j)

“The book is mainly devoted to variational methods in imaging. It is divided into three parts. … The book is interesting in particular for its rigorous presentation of many proved mathematical results, and is … important for the image processing community.” (Alessandro Duci, Zentralblatt MATH, Vol. 1177, 2010)


Table of contents (10 chapters)

  • Case Examples of Imaging

    Scherzer, Otmar (et al.)

    Pages 3-25

  • Image and Noise Models

    Scherzer, Otmar (et al.)

    Pages 27-49

  • Variational Regularization Methods for the Solution of Inverse Problems

    Scherzer, Otmar (et al.)

    Pages 53-113

  • Convex Regularization Methods for Denoising

    Scherzer, Otmar (et al.)

    Pages 115-158

  • Variational Calculus for Non-convex Regularization

    Scherzer, Otmar (et al.)

    Pages 159-183

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-0-387-69277-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.95
price for USA
  • ISBN 978-0-387-30931-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.95
price for USA
  • ISBN 978-1-4419-2166-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Variational Methods in Imaging
Authors
Series Title
Applied Mathematical Sciences
Series Volume
167
Copyright
2009
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-69277-7
DOI
10.1007/978-0-387-69277-7
Hardcover ISBN
978-0-387-30931-6
Softcover ISBN
978-1-4419-2166-6
Series ISSN
0066-5452
Edition Number
1
Number of Pages
XIV, 320
Topics