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: (1) Introduces variational methods with motivation from the deterministic, geometric, and stochastic point of view. (2) Bridges the gap between regularization theory in imageanalysis and in inverse problems. (3) Presents case examples in imaging to illustrate the use of variational methods e.g. denoising, thermoacoustics, computerized tomography. (4) Discusses link between non-convex calculus of variations, morphological analysis, and level set methods. (5) Analyses variational methods containing classical analysis of variational methods, modern analysis such as G-norm properties, and non-convex calculus of variations. (6) Uses numerical examples to enhance the theory. 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 Includes additional material and images online INDICE: Part I: Fundamentals of Imaging.- Case examples of imaging.- Imageand 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.
- ISBN: 978-0-387-30931-6
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 335
- Fecha Publicación: 01/11/2008
- Nº Volúmenes: 1
- Idioma: Inglés