Variational Methods in Imaging

• Main Authors: Scherzer, Otmar (Author), Grasmair, Markus (Author), Grossauer, Harald (Author), Haltmeier, Markus (Author), Lenzen, Frank (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2009.
• Series: Applied Mathematical Sciences, 167
• Subjects: Mathematics.; Radiology.; Image processing.; Numerical analysis.; Calculus of variations.; Calculus of Variations and Optimal Control; Optimization.; Image Processing and Computer Vision.; Signal, Image and Speech Processing.; Numerical Analysis.; Imaging / Radiology.

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, a...

Table of Contents:

• 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.