Title Variational methods in imaging / Otmar Scherzer [and others]

Published New York : Springer, ©2009

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Description 1 online resource (xiii, 320 pages) : illustrations Series Applied mathematical sciences ; v. 167 Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 167. Contents 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 Summary 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 Bibliography Includes bibliographical references (pages 287-307) and index Notes English Print version record In Springer eBooks Subject Imaging systems. Variational principles. Bildverarbeitung. Variationsrechnung. Bildgebendes Verfahren. Numerische Mathematik. Imaging systems. Variational principles. Imaging systems Variational principles Bildverarbeitung Variationsrechnung Bildgebendes Verfahren Numerische Mathematik Form Electronic book Author Scherzer, Otmar, 1964- LC no. 2008934867 ISBN 9780387692777 0387692770 9780387309316 0387309314

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