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Parabolic Quasilinear Equations Minimizing Linear Growth Functionals

  • Fuensanta Andreu-Vaillo
  • José M. Mazón
  • Vicent Caselles

Part of the Progress in Mathematics book series (PM, volume 223)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Fuensanta Andreu-Vaillo, José M. Mazón, Vicent Caselles
    Pages 1-30
  3. Fuensanta Andreu-Vaillo, José M. Mazón, Vicent Caselles
    Pages 31-56
  4. Fuensanta Andreu-Vaillo, José M. Mazón, Vicent Caselles
    Pages 57-79
  5. Fuensanta Andreu-Vaillo, José M. Mazón, Vicent Caselles
    Pages 81-123
  6. Fuensanta Andreu-Vaillo, José M. Mazón, Vicent Caselles
    Pages 125-162
  7. Fuensanta Andreu-Vaillo, José M. Mazón, Vicent Caselles
    Pages 163-212
  8. Fuensanta Andreu-Vaillo, José M. Mazón, Vicent Caselles
    Pages 213-269
  9. Back Matter
    Pages 271-342

About this book

Introduction

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.

Keywords

Approximation Calculus of variations Dirichlet problem Image restoration Neumann problem Nonlinear semigroups Parabolic equations partial differential equation

Authors and affiliations

  • Fuensanta Andreu-Vaillo
    • 1
  • José M. Mazón
    • 1
  • Vicent Caselles
    • 2
  1. 1.Departamento de Análisis MatemáticoUniversitat de ValenciaBurjassot (Valencia)Spain
  2. 2.Departamento de TecnologíaUniversitat Pompeu FabraBarcelonaSpain

Bibliographic information

  • 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
  • Print ISBN 978-3-0348-9624-5
  • Online ISBN 978-3-0348-7928-6
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site