Abstract
In this paper we derive a unified framework for the taut-string algorithm and regularization with G-norm data fit. The G-norm data fit criterion (popularized in image processing by Y. Meyer) has been paid considerable interest in regularization models for pattern recognition. The first numerical work based on G-norm data fit has been proposed by Osher and Vese. The taut-string algorithm has been developed in statistics (Mammen and van de Geer and Davies and Kovac) for denoising of one dimensional sample data of a discontinuous function. Recently Hinterberger et al. proposed an extension of the taut-string algorithm to higher dimensional data by introducing the concept of tube methods. Here we highlight common features between regularization programs with a G-norm data fit term and taut-string algorithms (respectively tube methods). This links the areas of statistics, regularization theory, and image processing.
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Otmar Scherzer received his Ph.D. in Mathematics from the University of Linz, Austria, in 1990. Till 1999 he has been at the Industrial Mathematics Institute at the University of Linz. From 1999–2000 he visited the University of Munich (Germany) and from 2000–2001 he was Professor at the University of Bayreuth (Germany). Since 2001 he is Professor at the Department of Computer Science at the University of Innsbruck (Austria). From 1995 to 1996 he had an Erwin Schrödinger Scholarship of the Austrian Science Foundation (FWF) for visiting Texas A&M University and the University of Delaware (USA). Otmar Scherzer received the Award of the Austrian Mathematical Society (1998) and the START-price of the FWF in (1999). He is in the editorial board of Numerical Functional Analysis and Optimization and Inverse Problems. His research interest include image processing and inverse problems.
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Scherzer, O. Taut-String Algorithm and Regularization Programs with G-Norm Data Fit. J Math Imaging Vis 23, 135–143 (2005). https://doi.org/10.1007/s10851-005-6462-1
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DOI: https://doi.org/10.1007/s10851-005-6462-1