Abstract
We consider the inverse problem associated with iterated function system with greyscale maps (IFSM): Given a target function f, find an IFSM, such that its fixed point \(\bar{f}\) is sufficiently close to f in the \(L^p\) distance. In this paper, we extend the collage-based method by adding a total variation term to the collage distance, with the notion that the solution to this modified minimization problem turns out to be less noisy than the one without this term. Numerical experiments are provided.
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Acknowledgements
This research was partially supported by Natural Sciences and Engineering Research Council of Canada (NSERC) in the form of a Discovery Grant (HK).
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Kunze, H., La Torre, D. (2018). Inverse Problems and Total Variation Minimization for Iterated Function Systems on Maps. In: Kilgour, D., Kunze, H., Makarov, R., Melnik, R., Wang, X. (eds) Recent Advances in Mathematical and Statistical Methods . AMMCS 2017. Springer Proceedings in Mathematics & Statistics, vol 259. Springer, Cham. https://doi.org/10.1007/978-3-319-99719-3_9
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