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 nite lattices.
