The recently introduced second order total generalised variation functional TGV2 β,α has been a successful regulariser for image processing purposes. Its definition involves two positive parameters α and β whose values determine the amount and the quality of the regularisation. In this paper we report on the behaviour of TGV2 β,α in the cases where the parameters α, β as well as their ratio β/α becomes very large or very small. Among others, we prove that for sufficiently symmetric two dimensional data and large ratio β/α, TGV2 β,α regularisation coincides with total variation (TV) regularization
CITATION STYLE
Papafitsoros, K., & Valkonen, T. (2015). Asymptotic behaviour of total generalised variation. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9087, pp. 702–714). Springer Verlag. https://doi.org/10.1007/978-3-319-18461-6_56
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