Infimal Convolution Regularisation Functionals of $$\mathrm {BV}$$ and $$\mathrm {L}^{p}$$ Spaces. The Case $$p=\infty $$
Abstract
In this paper we analyse an infimal convolution type regularisation functional called $$\mathrm {TVL}^{\infty }$$, based on the total variation ($$\mathrm {TV}$$) and the $$\mathrm {L}^{\infty }$$ norm of the gradient. The functional belongs to a more general family of $$\mathrm {TVL}^{p}$$ functionals ($$1
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