With its mathematically rigorous presentation, this book is a detailed treatment of the approach from an inverse problems point of view. It is geared towards graduate students and researchers in applied mathematics and can serve as a text for graduate courses.

This book focuses on variational methods in imaging science. Many numerical examples accompany the theory throughout the text. This systematic presentation includes additional material and images available on the website. It is geared towards graduate students and researchers in applied mathematics. Researchers in the area of imaging science will also find this book appealing. It can serve as a main text in courses in image processing or as a supplemental text for courses on regularization and inverse problems at the graduate level.

Introduces variational methods with motivation from the deterministic, geometric and stochastic point of view Presents case examples in imaging to illustrate the use of variational methods e.g. denoising, thermoacoustics, computerized tomography Discusses link between noncovex 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 nonconvex calculus of variations Includes additional material and images online Includes supplementary material: sn.pub/extras

Klappentext

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.