On the existence of weak solutions for a curvature driven elliptic system applied to image inpainting

Kehan Shi; Zhichang Guo

doi:10.1016/j.aml.2019.106003

On the existence of weak solutions for a curvature driven elliptic system applied to image inpainting

Kehan Shi
, Zhichang Guo^*

^*Corresponding author for this work

School of Mathematics

China Jiliang University

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

In this paper, an elliptic system consisting of a weighted total variation (TV) equation and a linear equation is proposed as an approximation of Euler's elastica image inpainting model. The existence of weak solutions for the system is proved by treating the TV term as the limit p→1⁺ of the p-Laplacian term. Numerical experiments show the connectivity of the proposed system for image inpainting.

Original language	English
Article number	106003
Journal	Applied Mathematics Letters
Volume	99
DOIs	https://doi.org/10.1016/j.aml.2019.106003
State	Published - Jan 2020

Keywords

Elliptic system
Image inpainting
Weighted TV equation

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10.1016/j.aml.2019.106003

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title = "On the existence of weak solutions for a curvature driven elliptic system applied to image inpainting",

abstract = "In this paper, an elliptic system consisting of a weighted total variation (TV) equation and a linear equation is proposed as an approximation of Euler's elastica image inpainting model. The existence of weak solutions for the system is proved by treating the TV term as the limit p→1+ of the p-Laplacian term. Numerical experiments show the connectivity of the proposed system for image inpainting.",

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note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Ltd",

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doi = "10.1016/j.aml.2019.106003",

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AU - Shi, Kehan

AU - Guo, Zhichang

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AB - In this paper, an elliptic system consisting of a weighted total variation (TV) equation and a linear equation is proposed as an approximation of Euler's elastica image inpainting model. The existence of weak solutions for the system is proved by treating the TV term as the limit p→1+ of the p-Laplacian term. Numerical experiments show the connectivity of the proposed system for image inpainting.

KW - Elliptic system

KW - Image inpainting

KW - Weighted TV equation

UR - https://www.scopus.com/pages/publications/85070675547

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DO - 10.1016/j.aml.2019.106003

M3 - 文章

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VL - 99

JO - Applied Mathematics Letters

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M1 - 106003

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On the existence of weak solutions for a curvature driven elliptic system applied to image inpainting

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Keywords

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