Generalizations of the Taut String Method

The taut string method is classically used in statistical applications to obtain a sparse estimation for a density given by point measurements. Mostly, a discrete formulation is employed that interpretes the data and the output as piecewise constant splines. This paper deals with the continuous form...

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Veröffentlicht in:Numerical functional analysis and optimization Jg. 29; H. 3-4; S. 346 - 361
Hauptverfasser: Grasmair, Markus, Obereder, Andreas
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Taylor & Francis Group 01.03.2008
Schlagworte:
Constrained minimization
Total variation
Tube method
Variational regularization
ISSN:0163-0563, 1532-2467
Online-Zugang:Volltext
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Zusammenfassung:The taut string method is classically used in statistical applications to obtain a sparse estimation for a density given by point measurements. Mostly, a discrete formulation is employed that interpretes the data and the output as piecewise constant splines. This paper deals with the continuous formulation of this algorithm. We show that it is able to deal with continuous data as well as with discrete data interpreted as Dirac measures. In fact, any one-dimensional finite signed Radon measure is suited as input for the method. Moreover, we study the usage of tubes of nonconstant diameter. Examples indicate that such tubes can be useful in various applications. An existence and uniqueness theorem is given for the continuous formulation of the taut string algorithm with arbitrary tubes of nonnegative diameter.
Bibliographie:ObjectType-Article-2
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content type line 23
ISSN:0163-0563
1532-2467
DOI:10.1080/01630560801998211