JSM 2011 Online Program

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Abstract Details

Activity Number: 520
Type: Contributed
Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract - #303444
Title: Spatial statistics, image analysis and percolation theory
Author(s): Mikhail Langovoy*+ and Michael Habeck and Bernhard Schoelkopf
Companies: Max Planck Institute for Biological Cybernetics and Max Planck Institute for Biological Cybernetics and Max Planck Institute for Developmental Biology and Max Planck Institute for Biological Cybernetics and Max Planck Institute for Developmental Biology
Address: Max Planck Institute for Developmental Biology, Tuebingen, , Germany
Keywords: Statistics of networks ; spatial statistics ; multiple testing ; image analysis ; percolation theory ; shape constraints
Abstract:

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. 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.


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