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In this paper we study the one dimensional second order total generalised variation regularisation (TGV) problem with $L^{2}$ data fitting term.
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K. Bredies, K. Kunisch, and T. Pock, Total generalized variation , SIAM Journal on Imaging Sciences 3
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Martin Benning, Christoph Brune, Martin Burger, and Jahn Müller, Higher-order TV methods – Enhancement via Bregman iteration , Journal of Scientific Computing 54
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Kristian Bredies, Karl Kunisch, and Tuomo Valkonen, Properties of L 1 -TGV 2 : The one-dimensional case , Journal of Mathematical Analysis and Applications 398
2013
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by same author, Exact solutions of one-dimensional TGV , preprint (2013)
2013
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