On the existence of weak solutions for a curvature driven elliptic system applied to image inpainting. (January 2020)

• Record Type: Journal Article
• Authors: Shi, Kehan; Guo, Zhichang
• Is Part Of: Applied mathematics letters. Volume 99(2020)
• Publication Date: 2020-01
• Subjects: Image inpainting -- Elliptic system -- Weighted TV equation; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2019.106003
• Languages: English
• ISSNs: 0893-9659

Abstract

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.