Overview
- Introduces variational methods with motivation from the deterministic, geometric and stochastic point of view
- Presents case examples in imaging to illustrate the use of variational methods e.g. denoising, thermoacoustics, computerized tomography
- Discusses link between noncovex 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Applied Mathematical Sciences (AMS, volume 167)
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Table of contents (10 chapters)
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Front Matter
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Fundamentals of Imaging
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Front Matter
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Mathematical Foundations
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Front Matter
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Back Matter
Keywords
About this book
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)
Authors and Affiliations
Bibliographic Information
Book Title: Variational Methods in Imaging
Authors: Otmar Scherzer, Markus Grasmair, Harald Grossauer, Markus Haltmeier, Frank Lenzen
Series Title: Applied Mathematical Sciences
DOI: https://doi.org/10.1007/978-0-387-69277-7
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag New York 2009
Hardcover ISBN: 978-0-387-30931-6Published: 09 October 2008
Softcover ISBN: 978-1-4419-2166-6Published: 19 November 2010
eBook ISBN: 978-0-387-69277-7Published: 26 September 2008
Series ISSN: 0066-5452
Series E-ISSN: 2196-968X
Edition Number: 1
Number of Pages: XIV, 320
Topics: Calculus of Variations and Optimal Control; Optimization, Image Processing and Computer Vision, Signal, Image and Speech Processing, Numerical Analysis, Imaging / Radiology