License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2017.23
URN: urn:nbn:de:0030-drops-72133
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7213/
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Buchet, Mickael ; Dey, Tamal K. ; Wang, Jiayuan ; Wang, Yusu

Declutter and Resample: Towards Parameter Free Denoising

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LIPIcs-SoCG-2017-23.pdf (1 MB)

Abstract

In many data analysis applications the following scenario is commonplace: we are given a point set that is supposed to sample a hidden ground truth K in a metric space, but it got corrupted with noise so that some of the data points lie far away from K creating outliers also termed as ambient noise. One of the main goals of denoising algorithms is to eliminate such noise so that the curated data lie within a bounded Hausdorff distance of K. Popular denoising approaches such as deconvolution and thresholding often require the user to set several parameters and/or to choose an appropriate noise model while guaranteeing only asymptotic convergence. Our goal is to lighten this burden as much as possible while ensuring theoretical guarantees in all cases.

Specifically, first, we propose a simple denoising algorithm that requires only a single parameter but provides a theoretical guarantee on the quality of the output on general input points. We argue that this single parameter cannot be avoided. We next present a simple algorithm that avoids even this parameter by paying for it with a slight strengthening of the sampling condition on the input points which is not unrealistic. We also provide some preliminary empirical evidence that our algorithms
are effective in practice.

BibTeX - Entry

@InProceedings{buchet_et_al:LIPIcs:2017:7213,
  author =	{Mickael Buchet and Tamal K. Dey and Jiayuan Wang and Yusu Wang},
  title =	{{Declutter and Resample: Towards Parameter Free Denoising}},
  booktitle =	{33rd International Symposium on Computational Geometry (SoCG 2017)},
  pages =	{23:1--23:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-038-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{77},
  editor =	{Boris Aronov and Matthew J. Katz},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7213},
  URN =		{urn:nbn:de:0030-drops-72133},
  doi =		{10.4230/LIPIcs.SoCG.2017.23},
  annote =	{Keywords: denoising, parameter free, k-distance,compact sets}
}

Keywords: denoising, parameter free, k-distance,compact sets
Collection: 33rd International Symposium on Computational Geometry (SoCG 2017)
Issue Date: 2017
Date of publication: 20.06.2017

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