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
• Language: English
• Published: New York, NY : Springer New York, 2009.
• Series: Applied Mathematical Sciences, 167
• Subjects: Mathematics.; Radiology, Medical.; Computer vision.; Numerical analysis.; Mathematical optimization.; Calculus of Variations and Optimal Control; Optimization.; Image Processing and Computer Vision.; Signal, Image and Speech Processing.; Numerical Analysis.; Imaging / Radiology.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-387-69277-7

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:

• 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.