About this book
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.
- Book Title Parabolic Quasilinear Equations Minimizing Linear Growth Functionals
- Series Title Progress in Mathematics
- Series Abbreviated Title Progress in Mathematics(Birkhäuser)
- DOI https://doi.org/10.1007/978-3-0348-7928-6
- Copyright Information Birkhäuser Verlag 2004
- Publisher Name Birkhäuser, Basel
- eBook Packages Springer Book Archive
- Hardcover ISBN 978-3-7643-6619-3
- Softcover ISBN 978-3-0348-9624-5
- eBook ISBN 978-3-0348-7928-6
- Series ISSN 0743-1643
- Series E-ISSN 2296-505X
- Edition Number 1
- Number of Pages XIV, 342
- Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
Partial Differential Equations
Approximations and Expansions
Calculus of Variations and Optimal Control; Optimization
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"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."
"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."
"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