@article{1101.68927,
author="Hinterberger, Walter and Hinterm\"uller, Michael and Kunisch, Karl and
    von Oehsen, Markus and Scherzer, Otmar",
title="{Tube methods for BV regularization.}",
language="English",
journal="J. Math. Imaging Vis. ",
volume="19",
number="3",
pages="219-235",
year="2003",
doi={10.1023/A:1026276804745},
abstract="{Summary: In this paper tube methods for reconstructing discontinuous
    data from noisy and blurred observation data are considered. It is shown
    that discrete bounded variation (BV)-regularization (commonly used in
    inverse problems and image processing) and the taut-string algorithm
    (commonly used in statistics) select reconstructions in a tube. A version of
    the taut-string algorithm applicable for higher dimensional data is
    proposed. This formulation results in a bilateral contact problem which can
    be solved very efficiently using an active set strategy. As a by-product it
    is shown that the Lagrange multiplier of the active set strategy is an
    efficient parameter for edge detection.}",
keywords="{Filtering; regularization; bounded variation; segmentation;
    taut-string algorithm}",
classmath="{*68U10 (Image processing)
}",
}