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Global Solvability of Constrained Singular Diffusion Equation Associated with Essential Variation
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 |
Publisher: | Department of Mathematics, Hokkaido University |
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
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Submitter: 数学紀要登録作業用
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