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  Statistical Image Analysis and Percolation Theory

Langovoy, M., Habeck, M., & Schölkopf, B. (2011). Statistical Image Analysis and Percolation Theory. In 2011 Joint Statistical Meetings (JSM).

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-BAEE-D Version Permalink: http://hdl.handle.net/21.11116/0000-0002-5453-2
Genre: Meeting Abstract

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 Creators:
Langovoy, M1, 2, Author              
Habeck, M1, 2, Author              
Schölkopf, B1, 2, Author              
Affiliations:
1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

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 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 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 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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 Dates: 2011-08
 Publication Status: Published online
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 Identifiers: BibTex Citekey: LangovoyHS2011
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Title: 2011 Joint Statistical Meetings (JSM)
Place of Event: Miami Beach, FL, USA
Start-/End Date: 2011-07-30 - 2011-08-04
Invited: Yes

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Title: 2011 Joint Statistical Meetings (JSM)
Source Genre: Proceedings
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Pages: - Volume / Issue: - Sequence Number: 520 Start / End Page: - Identifier: -