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Global Solvability of Constrained Singular Diffusion Equation Associated with Essential Variation

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83928

Title: Global Solvability of Constrained Singular Diffusion Equation Associated with Essential Variation
Authors: Giga, Yoshikazu Browse this author
Kuroda, Hirotoshi Browse this author
Yamazaki, Noriaki Browse this author
Keywords: Singular diffusion
total variation
color image processing
subdifferential
Issue Date: 2006
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 778
Start Page: 1
End Page: 10
Abstract: We consider a gradient flow system of total variation with constraint. Our system is often used in the color image processing to remove a noise from picture. In particular, we want to preserve the sharp edges of picture and color chromaticity. Therefore, the values of solutions to our model is constrained in some fixed compact Riemannian manifold. By this reason, it is very difficult to analyze such a problem, mathematically. The main object of this paper is to show the global solvability of a constrained singular diffusion equation associated with total variation. In fact, by using abstract convergence theory of convex functions, we shall prove the existence of solutions to our models with piecewise constant initial and boundary data.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69586
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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