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Spatial statistics, image analysis and percolation theory


Conference Paper


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.

Author(s): Langovoy, M. and Habeck, M. and Schölkopf, B.
Pages: 11
Year: 2011
Month: August
Day: 0
Publisher: American Statistical Association

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

Event Name: 2011 Joint Statistical Meetings (JSM)
Event Place: Miami Beach, FL, USA

Address: Alexandria, VA, USA
ISBN: 978-0-9839375-0-0

Links: PDF


  title = {Spatial statistics, image analysis and percolation theory},
  author = {Langovoy, M. and Habeck, M. and Sch{\"o}lkopf, B.},
  pages = {11},
  publisher = {American Statistical Association},
  address = {Alexandria, VA, USA},
  month = aug,
  year = {2011},
  month_numeric = {8}