Taut-String Algorithm and Regularization Programs with G-Norm Data Fit

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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