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Randomized algorithms for statistical image analysis based on percolation theory

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons84039

Langovoy,  M
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Davies, P., Langovoy, M., & Wittich, O. (2009). Randomized algorithms for statistical image analysis based on percolation theory. Talk presented at 27th European Meeting of Statisticians (EMS 2009). Toulouse, France.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-C445-D
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.