Infimal Convolution Regularisation Functionals of BV and L p Spaces. The Case p
Martin Burger, Konstantinos Papafitsoros, Evangelos Papoutsellis, Carola‐Bibiane Schönlieb · 2015
Abstract. In this paper we analyse an infimal convolution type regular-isation 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 recon-structed 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.