Multiple testing, uncertainty and realistic pictures

Details Multiple testing, uncertainty and realistic pictures Multiple testing, uncertainty and realistic pictures

2011-02-23

arxiv.org/abs/1102.4820v1

Mathematics

Statistics Theory

This paper initially appeared in January 2011 as EURANDOM Report 2011-004. Link to the abstract at EURANDOM Repository: http

Scientific paper

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 finite lattices.

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