Variational Methods in Imaging
(Sprache: Englisch)
With its mathematically rigorous presentation, this book is a detailed treatment of the approach from an inverse problems point of view. It is geared towards graduate students and researchers in applied mathematics and can serve as a text for graduate courses.
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With its mathematically rigorous presentation, this book is a detailed treatment of the approach from an inverse problems point of view. It is geared towards graduate students and researchers in applied mathematics and can serve as a text for graduate courses.
Klappentext zu „Variational Methods in Imaging “
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.
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. Many numerical examples accompany the theory throughout the text. It is geared towards graduate students and researchers in applied mathematics. Researchers in the area of imaging science will also find this book appealing. It can serve as a main text in courses in image processing or as a supplemental text for courses on regularization and inverse problems at the graduate level.
Inhaltsverzeichnis zu „Variational Methods in Imaging “
Fundamentals of Imaging.- Case Examples of Imaging.- Image and Noise Models.- Regularization.- Variational Regularization Methods for the Solution of Inverse Problems.- Convex Regularization Methods for Denoising.- Variational Calculus for Non-convex Regularization.- Semi-group Theory and Scale Spaces.- Inverse Scale Spaces.- Mathematical Foundations.- Functional Analysis.- Weakly Differentiable Functions.- Convex Analysis and Calculus of Variations.
Bibliographische Angaben
- Autoren: Otmar Scherzer , Markus Grasmair , Harald Grossauer , Markus Haltmeier , Frank Lenzen
- 2010, XIV, 320 Seiten, 72 Abbildungen, Masse: 16,4 x 23,9 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 1441921664
- ISBN-13: 9781441921666
Sprache:
Englisch
Pressezitat
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)
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