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＜E-Book＞
Variational Methods in Imaging / by Otmar Scherzer, Markus Grasmair, Harald Grossauer, Markus Haltmeier, Frank Lenzen
(Applied Mathematical Sciences. ISSN:2196968X ; 167)

Edition	1st ed. 2009.
Publisher	New York, NY : Springer New York : Imprint: Springer
Year	2009
Language	English
Size	XIV, 320 p : online resource
Authors	*Scherzer, Otmar author Grasmair, Markus author Grossauer, Harald author Haltmeier, Markus author Lenzen, Frank author SpringerLink (Online service)
Subjects	LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:Computer vision LCSH:Signal processing LCSH:Numerical analysis LCSH:Radiology FREE:Calculus of Variations and Optimization FREE:Computer Vision FREE:Signal, Speech and Image Processing FREE:Numerical Analysis FREE:Radiology
Notes	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 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 HTTP:URL=https://doi.org/10.1007/978-0-387-69277-7

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