Abstract
The recently introduced second order total generalised variation functional \(\mathrm{TGV}^{2}_{\beta ,\alpha }\) has been a successful regulariser for image processing purposes. Its definition involves two positive parameters \(\alpha \) and \(\beta \) whose values determine the amount and the quality of the regularisation. In this paper we report on the behaviour of \(\mathrm{TGV}^{2}_{\beta ,\alpha }\) in the cases where the parameters \(\alpha , \beta \) as well as their ratio \(\beta /\alpha \) becomes very large or very small. Among others, we prove that for sufficiently symmetric two dimensional data and large ratio \(\beta /\alpha \), \(\mathrm{TGV}^{2}_{\beta ,\alpha }\) regularisation coincides with total variation (\(\mathrm{TV}\)) regularisation.
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Papafitsoros, K., Valkonen, T. (2015). Asymptotic Behaviour of Total Generalised Variation. In: Aujol, JF., Nikolova, M., Papadakis, N. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2015. Lecture Notes in Computer Science(), vol 9087. Springer, Cham. https://doi.org/10.1007/978-3-319-18461-6_56
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DOI: https://doi.org/10.1007/978-3-319-18461-6_56
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