Abstract
A recent result by Łasica, Moll and Mucha about the \(\ell ^1\)-anisotropic Rudin-Osher-Fatemi model in \(\mathbb {R}^2\) asserts that the solution is piecewise constant on a rectilinear grid, if the datum is. By means of a new proof we extend this result to \(\mathbb {R}^n\). The core of our proof consists in showing that averaging operators associated to certain rectilinear grids map subgradients of the \(\ell ^1\)-anisotropic total variation seminorm to subgradients.
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Acknowledgements
We acknowledge support by the Austrian Science Fund (FWF) within the national research network “Geometry \(+\) Simulation,” S117, subproject 4.
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Kirisits, C., Scherzer, O., Setterqvist, E. (2019). Preservation of Piecewise Constancy under TV Regularization with Rectilinear Anisotropy. In: Lellmann, J., Burger, M., Modersitzki, J. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2019. Lecture Notes in Computer Science(), vol 11603. Springer, Cham. https://doi.org/10.1007/978-3-030-22368-7_40
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DOI: https://doi.org/10.1007/978-3-030-22368-7_40
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