Variational Methods in Imaging

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, such as denoising, thermoacoustics, and computerized tomography.
• Discusses the link between non-convex calculus of variations, morphological analysis, and level set methods.
• Analyzes 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.