The Convergence of a Central-Difference Discretization of Rudin-Osher-Fatemi Model for Image Denoising

Authors:
Ming-Jun Lai;Bradley Lucier;Jingyue Wang
Affiliations:
University of Georgia, Athens, USA GA 30602;Purdue University, West Lafayette, USA IN 47907;University of Georgia, Athens, USA GA 30602
Venue:
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Year:
2009

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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.