Spatial statistics, image analysis and percolation theory
Mikhail Langovoy, Michael Habeck and Bernhard Schölkopf
In: 2011 Joint Statistical Meetings (JSM)(2011).
We develop a novel method for detection of signals and reconstruction of images in the presence of random noise. The method uses results from percolation theory. We specifically address the problem of detection of multiple objects of unknown shapes in the case of nonparametric noise. The noise density is unknown and can be heavy-tailed. The objects of interest have unknown varying
intensities. No boundary shape constraints are imposed on the objects, only a set of weak bulk conditions is required. We view the object detection problem as a multiple hypothesis testing for discrete statistical inverse problems. We present an algorithm that allows to detect greyscale objects of various shapes in noisy images. We prove results on consistency and algorithmic complexity of
our procedures. Applications to cryo-electron microscopy are presented.