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Empirical Inference Talk 2009

Randomized algorithms for statistical image analysis based on percolation theory

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Empirical Inference
Mikhail Langovoy

We propose a novel probabilistic method for detection of signals and reconstruction of images in the presence of random noise. The method uses results from percolation and random graph theories (see Grimmett (1999)). We address the problem of detection and estimation of signals in situations where the signal-to-noise ratio is particularly low. We present an algorithm that allows to detect objects of various shapes in noisy images. The algorithm has linear complexity and exponential accuracy. Our algorithm substantially di ers from wavelets-based algorithms (see Arias-Castro et.al. (2005)). Moreover, we present an algorithm that produces a crude estimate of an object based on the noisy picture. This algorithm also has linear complexity and is appropriate for real-time systems. We prove results on consistency and algorithmic complexity of our procedures.

Author(s): Davies, PL. and Langovoy, M. and Wittich, O.
Links:
Year: 2009
Month: July
Day: 0
Bibtex Type: Talk (talk)
Digital: 0
Electronic Archiving: grant_archive
Event Name: 27th European Meeting of Statisticians (EMS 2009)
Event Place: Toulouse, France

BibTex 

@talk{DaviesL2009,
  title = {Randomized algorithms for statistical image analysis based on percolation theory},
  abstract = {We propose a novel probabilistic method for detection of signals and reconstruction
  of images in the presence of random noise. The method uses results from percolation
  and random graph theories (see Grimmett (1999)). We address the problem of
  detection and estimation of signals in situations where the signal-to-noise ratio is
  particularly low.
  We present an algorithm that allows to detect objects of various shapes in
  noisy images. The algorithm has linear complexity and exponential accuracy. Our
  algorithm substantially diers from wavelets-based algorithms (see Arias-Castro
  et.al. (2005)). Moreover, we present an algorithm that produces a crude estimate
  of an object based on the noisy picture. This algorithm also has linear complexity
  and is appropriate for real-time systems. We prove results on consistency and algorithmic
  complexity of our procedures.},
  month = jul,
  year = {2009},
  slug = {daviesl2009},
  author = {Davies, PL. and Langovoy, M. and Wittich, O.},
  month_numeric = {7}
}