Hokkaido University | Library | HUSCAP Advanced Search 言語 日本語 English

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

Files in This Item:
 pre693.pdf 246.61 kB PDF View/Open
 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