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Partial regularity for a selective smoothing functional for image restoration in BV space

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83844

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
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

Submitter: 数学紀要登録作業用

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