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.

Inhalt

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.