Characterization of the Solution of Linear Inverse Problems with Generalized TV Regularization
M. Unser
Proceedings of Imaging and Applied Optics: OSA Optics & Photonics Congress, Mathematics in Imaging (OSA-MI'16), Heidelberg, Federal Republic of Germany, July 25-28, 2016, paper no. MW5H.1.
Ill-posed inverse problems are often constrained by imposing a bound on the total variation of the solution. Here, we consider a generalized version of total-variation regularization that is tied to some differential operator L. We then show that the general form of the solution is a nonuniform L-spline with fewer knots than the number of measurements.
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AUTHOR="Unser, M.",
TITLE="Characterization of the Solution of Linear Inverse Problems with
Generalized {TV} Regularization",
BOOKTITLE="Proceedings of Imaging and Applied Optics: {OSA} Optics \&
Photonics Congress, Mathematics in Imaging ({OSA-MI'16})",
YEAR="2016",
editor="",
volume="",
series="",
pages="",
address="Heidelberg, Federal Republic of Germany",
month="June 25-28,",
organization="",
publisher="",
note="paper no.\ MW5H.1")
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