Abstract
We study the connection between minimizers of the discrete and the continuous Rudin-Osher-Fatemi models. We use a central-difference total variation term in the discrete ROF model and treat the discrete input data as a projection of the continuous input data into the discrete space. We employ a method developed in [13] with slight adaption to the setting of the central-difference total variation ROF model. We obtain an error bound between the discrete and the continuous minimizer in L 2 norm under the assumption that the continuous input data are in W 1, 2.
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Lai, MJ., Lucier, B., Wang, J. (2009). The Convergence of a Central-Difference Discretization of Rudin-Osher-Fatemi Model for Image Denoising. In: Tai, XC., Mørken, K., Lysaker, M., Lie, KA. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2009. Lecture Notes in Computer Science, vol 5567. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02256-2_43
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DOI: https://doi.org/10.1007/978-3-642-02256-2_43
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02255-5
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