Fractional total variation denoising model with L1 fidelity. (September 2022)

• Record Type: Journal Article
• Authors: Bessas, Konstantinos
• Is Part Of: Nonlinear analysis. Volume 222(2022)
• Publication Date: 2022-09
• Subjects: 49Q20 -- 94A08; Fractional total variation -- Fractional perimeter -- Image denoising -- Regularity of minimizers; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.112926
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study a nonlocal version of the total variation-based model with L 1 fidelity for image denoising, where the regularizing term is replaced with the fractional s -total variation. We discuss regularity of the level sets and uniqueness of solutions, both for high and low values of the fidelity parameter. We analyse in detail the case of binary data given by the characteristic functions of convex sets.