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Mathematics | Variational Methods in Imaging

Variational Methods in Imaging

Series: Applied Mathematical Sciences, Vol. 167

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

2009, XIV, 320 p.

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  • 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

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.

Content Level » Research

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

Related subjects » Computational Science & Engineering - Image Processing - Mathematics - Radiology - Signals & Communication

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