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Statistical image analysis and percolation theory

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Davies, P., Langovoy, M., & Wittich, O. (2010). Statistical image analysis and percolation theory. In 73rd Annual Meeting of the Institute of Mathematical Statistics (IMS 2010).


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-BF0C-3
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 objects of unknown shapes in the case of nonparametric noise. The noise density is unknown and can be heavy-tailed. We view the object detection problem as hypothesis testing for discrete statistical inverse problems. We present an algorithm that allows to detect objects of various shapes in noisy images. We prove results on consistency and algorithmic complexity of our procedures.