In this paper we analyse an infimal convolution type regularisation functional called TVL∞ , based on the total variation (TV) and the L ∞ norm of the gradient. The functional belongs to a more general family of TVLp functionals (1 < p ≤ ∞) introduced in [5]. There, the case 1 < p < ∞ is examined while here we focus on the p = ∞ case. We show via analytical and numerical results that the minimisation of the TVL∞ functional promotes piecewise affine structures in the reconstructed images similar to the state of the art total generalised variation (TGV) but improving upon preservation of hat–like structures. We also propose a spatially adapted version of our model that produces results comparable to TGV and allows space for further improvement.
CITATION STYLE
Burger, M., Papafitsoros, K., Papoutsellis, E., & Schönlieb, C. B. (2016). Infimal convolution regularisation functionals of BV and Lp spaces. The case p = ∞. In IFIP Advances in Information and Communication Technology (Vol. 494, pp. 169–179). Springer New York LLC. https://doi.org/10.1007/978-3-319-55795-3_15
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