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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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Author:J. Franke, S. Halim
URN (permanent link):urn:nbn:de:hbz:386-kluedo-15273
Serie (Series number):Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (106)
Document Type:Report
Language of publication:English
Year of Completion:2007
Year of Publication:2007
Publishing Institute:Fraunhofer-Institut für Techno- und Wirtschaftsmathematik
Date of the Publication (Server):2008/05/28
Tag:defect detection; kernel estimate; textile quality control; texture classification; wild bootstrap test
Faculties / Organisational entities:Fraunhofer (ITWM)
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011