Variational Methods in Imaging [electronic resource] /
by Otmar Scherzer, Markus Grasmair, Harald Grossauer, Markus Haltmeier, Frank Lenzen.
- XIV, 320 p. online resource.
- Applied Mathematical Sciences, 167 0066-5452 ; .
- Applied Mathematical Sciences, 167 .
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.
ZDB-2-SMA
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.
9780387692777
10.1007/978-0-387-69277-7 doi
Mathematics. Radiology, Medical. Computer vision. Numerical analysis. Mathematical optimization. Mathematics. Calculus of Variations and Optimal Control; Optimization. Image Processing and Computer Vision. Signal, Image and Speech Processing. Numerical Analysis. Imaging / Radiology.