Exact solutions to the total generalised variation minimisation problem

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Total generalised variation (TGV) was introduced by Bredies et al. as a high quality regulariser for variational problems arising in mathematical image processing like denoising and deblurring. The main advantage over the classical total variation regularisation is the elimination of the undesirable stairscasing effect. In this talk we will give a small introduction to TGV and provide some properties of the exact solutions to the L^{2}-TGV model in the one dimensional case.