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  Spatial statistics, image analysis and percolation theory

Langovoy, M., Habeck, M., & Schölkopf, B. (2011). Spatial statistics, image analysis and percolation theory. In 2011 Joint Statistical Meetings (JSM). Alexandria, VA, USA: American Statistical Association.

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Item Permalink: https://hdl.handle.net/21.11116/0000-000A-6E9A-E Version Permalink: https://hdl.handle.net/21.11116/0000-000A-6E9C-C
Genre: Conference Paper

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https://arxiv.org/pdf/1310.8574.pdf (Any fulltext)
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 Creators:
Langovoy, M1, Author           
Habeck, M1, Author           
Schölkopf, B, Author           
Affiliations:
1Department Protein Evolution, Max Planck Institute for Developmental Biology, Max Planck Society, ou_3375791              

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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. 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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 Dates: 2011-08
 Publication Status: Issued
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 Rev. Type: -
 Identifiers: BibTex Citekey: LangovoyHS2011_2
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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

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Title: 2011 Joint Statistical Meetings (JSM)
Source Genre: Proceedings
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Publ. Info: Alexandria, VA, USA : American Statistical Association
Pages: 11 Volume / Issue: - Sequence Number: - Start / End Page: - Identifier: ISBN: 978-0-9839375-0-0