โ Scribed by Otmar Scherzer, Markus Grasmair, Harald Grossauer, Markus Haltmeier, Frank Lenzen (auth.)
No coin nor oath required. For personal study only.
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.
Front Matter....Pages I-XIII
Front Matter....Pages 1-1
Case Examples of Imaging....Pages 3-25
Image and Noise Models....Pages 27-49
Front Matter....Pages 51-51
Variational Regularization Methods for the Solution of Inverse Problems....Pages 53-113
Convex Regularization Methods for Denoising....Pages 115-158
Variational Calculus for Non-convex Regularization....Pages 159-183
Semi-group Theory and Scale Spaces....Pages 185-203
Inverse Scale Spaces....Pages 205-218
Front Matter....Pages 219-219
Functional Analysis....Pages 221-238
Weakly Differentiable Functions....Pages 239-272
Convex Analysis and Calculus of Variations....Pages 273-286
Back Matter....Pages 287-320
Calculus of Variations and Optimal Control; Optimization; Image Processing and Computer Vision; Signal, Image and Speech Processing; Numerical Analysis; Imaging / Radiology
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