Error estimates for finite differences approximations of the total variation - Archive ouverte HAL Access content directly
Journal Articles IMA Journal of Numerical Analysis Year : 2022

Error estimates for finite differences approximations of the total variation

(1) , (1, 2)
1
2

Abstract

We present a convergence rate analysis of the Rudin-Osher-Fatemi (ROF) denoising problem for two different discretizations of the total variation. The first discretization is the well-known isotropic total variation that suffers from a blurring effect in a special diagonal direction. We prove that in the setting corresponding to this direction, the discrete ROF energy converges to the continuous one in O(h^2/3). The second total variation is based on Raviart-Thomas fields and achieves a O(h) convergence rate for the same quantity under some standard hypotheses.
Fichier principal
Vignette du fichier
CC-TV-rev.pdf (2.66 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-02539136 , version 1 (09-04-2020)
hal-02539136 , version 2 (07-10-2021)

Identifiers

Cite

Corentin Caillaud, Antonin Chambolle. Error estimates for finite differences approximations of the total variation. IMA Journal of Numerical Analysis, 2022, pp.drac001. ⟨10.1093/imanum/drac001⟩. ⟨hal-02539136v2⟩
326 View
160 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More