Abstract
In this paper, for certain classes of functions, we present analytical evaluations of double integral expressions representing approximations of the total variation seminorm. These calculations are carried out by using the Maple computer algebra software package in a sophisticated way.The derived expressions can be used for approximations of the total variation seminorm, and, in particular, can be used for efficient numerical total variation regularization energy minimization.
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Acknowledgements
The authors would like to express their gratitude to Paul F. X. Müller for introducing us to the recent work on the new characterizations of Sobolev spaces and BV and some stimulating discussions. This work has been supported by the Austrian Science Fund (FWF) within the national research networks Industrial Geometry, project 9203-N12, and Photoacoustic Imaging in Biology and Medicine, project S10505-N20. Moreover, the authors thank a referee for the careful reading of the manuscript and many detailed comments.
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Pontow, C., Scherzer, O. (2012). Analytical Evaluations of Double Integral Expressions Related to Total Variation. In: Langer, U., Paule, P. (eds) Numerical and Symbolic Scientific Computing. Texts & Monographs in Symbolic Computation. Springer, Vienna. https://doi.org/10.1007/978-3-7091-0794-2_10
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DOI: https://doi.org/10.1007/978-3-7091-0794-2_10
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