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Hokkaido University Preprint Series in Mathematics >
Partial regularity for a selective smoothing functional for image restoration in BV space
| Title: | Partial regularity for a selective smoothing functional for image restoration in BV space |
| Authors: | Chen, Yunmei Browse this author | | Rao, Murali Browse this author | | Tonegawa, Yoshihiro Browse this author | | Wunderli, T. Browse this author |
| Keywords: | bounded variation | | selective smooothing | | image processing | | image restoration | | noise removal | | partial regularity |
| Issue Date: | 2005 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 693 |
| Start Page: | 1 |
| End Page: | 19 |
| Abstract: | In this paper we study the partial regularity of a functional on BV space proposed by Chambolle and Lions [3] for the purposes of image restoration. The functional designed to smooth corrupted images using isotropic diffusion via the Laplacian where the gradients of the image are below a certain threshold \epsilon and retain edges where gradients are above the threshold using the total variation. Here we prove that if the solution $u \in BV$ of the model minimization problem, defined on an open set \Omega, is such that the Lebesgue measure of the set where the gradient of $u$ is below the threshold \epsilon is positive, then ther exists a non-empty open region $E$ for which $u \in C^{1,\alpha}$ on $E$ and $|\nabla u|<\epsilon$, and $|\nabla u| \geq \epsilon $ on $\Omega\setminus E $ a.e. Thus we indeed have smoothing where $|\nabla u|<\ \epsilon$. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69498 |
| 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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