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Parabolic Quasilinear Equations Minimizing Linear Growth Functionals : Progress in Mathematics - Fuensanta Andreu-Vaillo

Parabolic Quasilinear Equations Minimizing Linear Growth Functionals

Progress in Mathematics

Hardcover

Published: 26th January 2004
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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.

"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 fur Mathematik

Preface
Total Variation Based Image Restoration
The Neumann Problem for the Total Variation Flow
The Total Variation Flow in R[actual symbol not reproducible]N
Asymptotic Behaviour and Qualtitative Properties of Solutions
The Dirichlet Problem for the Total Variation Flow
Parabolic Equations Minimizing Linear Growth Functionals: L[actual symbol not reproducible]2-Theory
Parabolic Equations Minimizing Linear Growth Functionals: L[actual symbol not reproducible]1-Theory
Nonlinear Semigroups
Functions of Bounded Variation
Pairings Between Measures and Bounded Functions
References
Index
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783764366193
ISBN-10: 3764366192
Series: Progress in Mathematics
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 342
Published: 26th January 2004
Publisher: Birkhauser Verlag AG
Country of Publication: CH
Dimensions (cm): 23.5 x 15.5  x 1.91
Weight (kg): 0.7