caa a22 4500 467914680 CHVBK 20180406152858.0 cr unu---uuuuu 170328e20061201xx s 000 0 eng 10.1007/s11263-006-8066-7 doi (NATIONALLICENCE)springer-10.1007/s11263-006-8066-7 Splines in Higher Order TV Regularization [Elektronische Daten] [Gabriele Steidl, Stephan Didas, Julia Neumann] Splines play an important role as solutions of various interpolation and approximation problems that minimize special functionals in some smoothness spaces. In this paper, we show in a strictly discrete setting that splines of degree m−1 solve also a minimization problem with quadratic data term and m-th order total variation (TV) regularization term. In contrast to problems with quadratic regularization terms involving m-th order derivatives, the spline knots are not known in advance but depend on the input data and the regularization parameter λ. More precisely, the spline knots are determined by the contact points of the m-th discrete antiderivative of the solution with the tube of width 2λ around the m-th discrete antiderivative of the input data. We point out that the dual formulation of our minimization problem can be considered as support vector regression problem in the discrete counterpart of the Sobolev space W 2,0 m . From this point of view, the solution of our minimization problem has a sparse representation in terms of discrete fundamental splines. Springer Science + Business Media, LLC, 2006 higher order TV regularization nationallicence splines nationallicence support vector regression nationallicence Legendre-Fenchel dualization taut-string algorithm nationallicence Steidl Gabriele Faculty of Mathematics and Computer Science, University of Mannheim, 68131, Mannheim, Germany aut Didas Stephan Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, 66123, Saarbrücken, Germany aut Neumann Julia Faculty of Mathematics and Computer Science, University of Mannheim, 68131, Mannheim, Germany aut International Journal of Computer Vision Kluwer Academic Publishers 70/3(2006-12-01), 241-255 0920-5691 70:3<241 2006 70 11263 https://doi.org/10.1007/s11263-006-8066-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11263-006-8066-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Steidl Gabriele Faculty of Mathematics and Computer Science, University of Mannheim, 68131, Mannheim, Germany aut NATIONALLICENCE 700 1- Didas Stephan Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, 66123, Saarbrücken, Germany aut NATIONALLICENCE 700 1- Neumann Julia Faculty of Mathematics and Computer Science, University of Mannheim, 68131, Mannheim, Germany aut NATIONALLICENCE 773 0- International Journal of Computer Vision Kluwer Academic Publishers 70/3(2006-12-01), 241-255 0920-5691 70:3<241 2006 70 11263 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer