Variational Methods in Imaging

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Applied Mathematical Sciences 167

ISBN: 0387309314
ISBN 13: 9780387309316
Verlag: Springer Verlag GmbH
Umfang: xiv, 320 S., 72 s/w Illustr., 72 Fotos
Erscheinungsdatum: 09.10.2008
Weitere Autoren: Scherzer, Otmar/Grasmair, Markus/Grossauer, Harald et al
Auflage: 1/2009
Format: 2.2 x 24 x 16.1
Gewicht: 630 g
Produktform: Gebunden/Hardback
Einband: GEB

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 nonconvex calculus of variations, morphological analysis, and level set methods Analyses variational methods containing classical analysis of variational methods, modern analysis such as Gnorm properties, and nonconvex 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.

Artikelnummer: 1728458 Kategorie:

Beschreibung

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

Part I: Fundamentals of Imaging.- Case examples of imaging.- Image and Noise Models.- Part II: 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.- Part III: Mathematical Foundations.- Functional Analysis.- Weakly Differentiable Functions.- Convex Analysis and Calculus Variations.- Nomenclature.- References.- Index.

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