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First Order Quasi-Linear PDEs with BV Boundary Data and Applications to Image Inpainting

Thomas März

ISBN 978-3-8325-2639-9
187 pages, year of publication: 2010
price: 45.00 €
This book investigates the well-posedness of the mathematical model behind the method "Image Inpainting Based on Coherence Transport". Image inpainting methods serve the purpose of touching up damaged or unwanted elements of a digital picture. The model behind the mentioned method is a Dirichlet problem for a first order quasi-linear hyperbolic functional partial differential equation where all points of the boundary are inflow points. The main concern of this thesis is to proof the existence and the uniqueness of a solution to such kind of problems as well as the solutions's continuous dependence on the data. The general theory finally is used to obtain the well-posedness of the inpainting model.

Keywords:
  • Hyperbolic PDEs
  • Method of Characteristics
  • Bounded Variation
  • Functional PDEs
  • Fixed Point Theory

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