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Pré-Publication, Document De Travail Année : 2020

Error estimates for finite differences approximations of the total variation

Résumé

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.
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Dates et versions

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

Identifiants

  • HAL Id : hal-02539136 , version 1

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Corentin Caillaud, Antonin Chambolle. Error estimates for finite differences approximations of the total variation. 2020. ⟨hal-02539136v1⟩
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