Total generalized variation for piecewise constant functions on triangular meshes with applications in imaging

• Verfasst von: Baumgärtner, Lukas [VerfasserIn]
• Verfasst von: Bergmann, Ronny [VerfasserIn]
• Verfasst von: Herzog, Roland [VerfasserIn]
• Verfasst von: Schmidt, Stephan [VerfasserIn]
• Verfasst von: Vidal-Núnez, José [VerfasserIn]
• Titel: Total generalized variation for piecewise constant functions on triangular meshes with applications in imaging
• Verf.angabe: Lukas Baumgärtner, Ronny Bergmann, Roland Herzog, Stephan Schmidt, and José Vidal-Núnez
• E-Jahr: 2023
• Jahr: February 27, 2023
• Umfang: 27 S.
• Fussnoten: Gesehen am 17.05.2023
• Titel Quelle: Enthalten in: Society for Industrial and Applied MathematicsSIAM journal on imaging sciences
• Ort Quelle: Philadelphia, Pa. : SIAM, 2008
• Jahr Quelle: 2023
• Band/Heft Quelle: 16(2023), 1 vom: Feb., Seite 313-339
• ISSN Quelle: 1936-4954
• DOI: doi:10.1137/22M1505281
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1845625455

Abstract

Multiplicative noise removal problems have attracted much attention in recent years. Unlike additive noise removal problems, the noise is multiplied to the orginal image, so almost all information of the original image may disappear in the observed image. The main aim of this paper is to propose and study a strictly convex objective function for multiplicative noise removal problems. We also incorporate the modified total variation regularization in the objective function to recover image edges. We develop an alternating minimization algorithm to find the minimizer of such an objective function efficiently and also show the convergence of the minimizing method. Our experimental results show that the quality of images denoised by the proposed method is quite good.