Multiple testing, uncertainty and realistic pictures

M. Langovoy, O. Wittich

Research output: Book/ReportReportAcademic

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Abstract

We study statistical detection of grayscale objects in noisy images. The object of interest is of unknown shape and has an unknown intensity, that can be varying over the object and can be negative. No boundary shape constraints are imposed on the object, only a weak bulk condition for the object's interior is required. We propose an algorithm that can be used to detect grayscale objects of unknown shapes in the presence of nonparametric noise of unknown level. Our algorithm is based on a nonparametric multiple testing procedure. We establish the limit of applicability of our method via an explicit, closed-form, non-asymptotic and nonparametric consistency bound. This bound is valid for a wide class of nonparametric noise distributions. We achieve this by proving an uncertainty principle for percolation on fi??nite lattices.
Original languageEnglish
Place of PublicationEindhoven
PublisherEurandom
Number of pages21
Publication statusPublished - 2011

Publication series

NameReport Eurandom
Volume2011004
ISSN (Print)1389-2355

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