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01-07-2019 | REPRESENTATION, PROCESSING, ANALYSIS, AND UNDERSTANDING OF IMAGES | Issue 3/2019

Pattern Recognition and Image Analysis 3/2019

Adaptive Detection of Normal Mixture Signals with Pre-Estimated Gaussian Mixture Noise

Journal:
Pattern Recognition and Image Analysis > Issue 3/2019
Author:
A. K. Gorshenin
Important notes
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Andrey K. Gorshenin (born 1986) is Candidate of Science (PhD) in physics and mathematics (Probability theory and mathematical statistics, Lomonosov Moscow State University, 2011), associate professor (Mathematical modeling, numerical methods, and software systems, 2017), leading scientist, Institute of Informatics Problems, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences; leading scientist, Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University; senior scientist, P. P. Shirshov Institute of Oceanology of the Russian Academy of Sciences. Specialist degree with honor in applied mathematics and computer science (Faculty of Computational Mathematics and Cybernetics of Lomonosov Moscow State University, 2008). Fields of research priorities: probability theory, mathematical statistics, computer sciences, modelling of real processes, EM algorithms, method of moving separation of mixtures of probability distributions, Big Data, data visualization, mathematical modelling, neural networks. Author of 145 scientific papers and textbooks, 65 certificates RF of state registration of computer programs. Member of the Skolkovo Expert Panel (Moscow, Russia), Academic Expert of the National Research University Higher School of Economics (Moscow, Russia), Expert of the Russian Foundation for Basic Research (Moscow, Russia), Expert of the Russian Academy of Sciences (Moscow, Russia), External Expert of the Foundation for Assistance to Small Innovative Enterprises (Moscow, Russia). Member of the editorial boards of peer-reviewed journals “Informatika i ee primeneniya” (Scopus) and “Systems and Means оf Informatics”. Member of the Coordination Council for Youth Affairs in the Sphere of Science and Education under the Presidential Council for Science and Education. Awards: President Grant for Government Support of Young Russian Scientists (2014–2015), Russian Academy of Sciences Medal with the Prize for Young Scientists (2015), Scholarship of the President of the Russian Federation for Young Scientists and Postgraduates (2018–2020). Grant supervisor (Russian Science Foundation, Russian Foundation for Basic Research, President Grant for Government Support of Young Russian Scientists).

Abstract

The paper describes the adaptive method of estimating the parameters of the distribution of the useful signal under the assumption that the noise distribution can be pre-estimated. It is based on the method of moving separation of the finite normal mixtures and implemented for the estimating both signal-noise and signal distribution parameters. We assume that the probability distribution of the signal, signal with noise and “pure” noise can be presented in form of finite normal mixtures. Also, a method for change point detection based on testing the homogeneity hypothesis using the Kolmogorov criterion is proposed.

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