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 and can be heavy-tailed. 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 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.
Keywords: Spatial statistics; percolation theory; detection; nonparametric test
Biography: Dr. Mikhail Langovoy is a Research Scientist at the Max Planck Institute for Biological Cybernetics and at the Max Planck Institute for Developmental Biology in Tuebingen, Germany. He received his Master of Science degree in algebra and number theory from St Petersburg State University, Russia, in 2001, and a Ph. D. in statistics from the University of Goettingen, Germany, in 2007. After completing his thesis on data-driven tests of statistical hypothesis, he has been doing research on probability theory and stochastic analysis at the University of Bonn in Germany, and research on spatial statistics and image analisis at the European research institute EURANDOM in the Netherlands. At present, he is working in both stochastics and machine learning.