Parabolic Quasilinear Equations Minimizing Linear Growth Functionals

✍ Scribed by Fuensanta Andreu-Vaillo, José M. Mazón, Vicent Caselles (auth.)

• Publisher: Birkhäuser Basel
• Year: 2004
• Tongue: English
• Leaves: 350
• Series: Progress in Mathematics 223
• Edition: 1
• Category: Library

✦ Synopsis

Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2003.

This book contains a detailed mathematical analysis of the variational approach to image restoration based on the minimization of the total variation submitted to the constraints given by the image acquisition model. This model, initially introduced by Rudin, Osher, and Fatemi, had a strong influence in the development of variational methods for image denoising and restoration, and pioneered the use of the BV model in image processing. After a full analysis of the model, the minimizing total variation flow is studied under different boundary conditions, and its main qualitative properties are exhibited. In particular, several explicit solutions of the denoising problem are computed.

✦ Table of Contents

Front Matter....Pages i-xiv
Total Variation Based Image Restoration....Pages 1-30
The Neumann Problem for the Total Variation Flow....Pages 31-56
The Total Variation Flow in ℝ N ....Pages 57-79
Asymptotic Behaviour and Qualitative Properties of Solutions....Pages 81-123
The Dirichlet Problem for the Total Variation Flow....Pages 125-162
Parabolic Equations Minimizing Linear Growth Functionals: L 2 -Theory....Pages 163-212
Parabolic Equations Minimizing Linear Growth Functionals: L 1 -Theory....Pages 213-269
Back Matter....Pages 271-342

✦ Subjects

Partial Differential Equations; Approximations and Expansions; Functional Analysis; Visualization; Calculus of Variations and Optimal Control; Optimization