Parabolic Quasilinear Equations Minimizing Linear Growth Functionals

Fuensanta Andreu-Vaillo

ISBN 10: 3034896247 / ISBN 13: 9783034896245

Published by Birkhäuser Basel, 2012

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9783034896245

Bibliographic Details

• Title: Parabolic Quasilinear Equations Minimizing Linear Growth Functionals
• Publisher: Birkhäuser Basel
• Publication Date: 2012
• Language: English
• ISBN 10: 3034896247
• ISBN 13: 9783034896245
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 20D millimeters 235 millimeters width by 155 millimeters height by 20 millimeters depth
• Weight: 546 grams

About this title

Synopsis

This book covers with great detail the mathematical developments in total variation based image restauration. It contains a full analysis of quasilinear parabolic equations whose operator is in divergence form, being the subdifferential of a convex function of the modulus of the gradient.

The techniques can be used to justify many mathematical models appearing in different contexts like continuum mechanics, faceted crystal growth, and image processing. The book will be useful to graduate students and researchers in mathematics and image processing.

Review

"This book is well written...[and] should be of interest to anyone studying image reconstruction and to anyone in PDEs trying to see what kinds of modern applications abound for the subject."

―Mathematical Reviews

"This book is devoted to PDE's of elliptic and parabolic type associated to functionals having a linear growth in the gradient, with a special emphasis on the applications related to image restoration and nonlinear filters.... The book is written with great care, paying also a lot of attention to the bibliographical and historical notes. It is a recommended reading for all researchers interested in this field."

―Zentralblatt Math

"The goal of this mongraph is to present general existence and uniqueness results for quasilinear parabolic equations whose operator is the subdifferential of a convex Lagrangian which has linear growth. Special emphasis is given to the case of the minimizing total variational flow for which the Neumann, Dirichlet, and Cauchy problem are discussed. The developed techniques apply to problems in continuum mechanics, image restoration and faceted crystal growth."

---Monatshefte für Mathematik