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Wild bootstrap tests for comparing signals and images

  • In this expository article, we give an introduction into the basics of bootstrap tests in general. We discuss the residual-based and the wild bootstrap for regression models suitable for applications in signal and image analysis. As an illustration of the general idea, we consider a particular test for detecting differences between two noisy signals or images which also works for noise with variable variance. The test statistic is essentially the integrated squared difference between the signals after denoising them by local smoothing. Determining its quantile, which marks the boundary between accepting and rejecting the hypothesis of equal signals, is hardly possible by standard asymptotic methods whereas the bootstrap works well. Applied to the rows and columns of images, the resulting algorithm not only allows for the detection of defects but also for the characterization of their location and shape in surface inspection problems.

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Verfasserangaben:J. Franke, S. Halim
URN (Permalink):urn:nbn:de:hbz:386-kluedo-15273
Schriftenreihe (Bandnummer):Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (106)
Sprache der Veröffentlichung:Englisch
Jahr der Fertigstellung:2007
Jahr der Veröffentlichung:2007
Veröffentlichende Institution:Fraunhofer-Institut für Techno- und Wirtschaftsmathematik
Datum der Publikation (Server):28.05.2008
Freies Schlagwort / Tag:defect detection; kernel estimate; textile quality control; texture classification; wild bootstrap test
Fachbereiche / Organisatorische Einheiten:Fraunhofer (ITWM)
DDC-Sachgruppen:5 Naturwissenschaften und Mathematik / 510 Mathematik
Lizenz (Deutsch):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011