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01.10.2019 | MATHEMATICAL THEORY OF IMAGES AND SIGNALS REPRESENTING, PROCESSING, ANALYSIS, RECOGNITION AND UNDERSTANDING | Ausgabe 4/2019

Pattern Recognition and Image Analysis 4/2019

Generalized Spectral-Analytical Method and Its Applications in Image Analysis and Pattern Recognition Problems

Zeitschrift:
Pattern Recognition and Image Analysis > Ausgabe 4/2019
Autoren:
S. A. Makhortykh, L. I. Kulikova, A. N. Pankratov, R. K. Tetuev
Wichtige Hinweise
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Makhortykh Sergei Aleksandrovich. Born in 1963. Graduated from Moscow Physical–Technical Institute (Faculty of Aerophysics and Space Research) in 1986. Academic secretary of the Institute of Mathematical Problems of Biology (Branch of the Keldysh Institute of Applied Mathematics, Russian Academy of Sciences). Candidate in Physics and Mathematics since 1990. Scientific interests: spectral information-processing methods, bioinformatics, mathematical biology, environmental science, pattern recognition. Author of more than 60 reports and papers in peer-reviewed journals.
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Kulikova Ludmila Ivanovna. Born in 1960. Graduated from V.I. Ulyanov Lenin Kazan State University in 1982 (Faculty of Computational Mathematics and Cybernetics). Senior researcher of the Institute of Mathematical Problems of Biology (Branch of the Keldysh Institute of Applied Mathematics, Russian Academy of Sciences). Candidate in Physics and Mathematics, speciality 05.13.17 “Theoretical Foundations of Informatics” since 2007. Scintific interests: spectral-analytical information processing methods, data conversion, bioinformatics, pattern recognition. Author of more than 30 papers in journals.
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Pankratov Anton Nikolaevich. Born in 1972. Graduated from Moscow State University (Faculty of Computational Mathematica and Cybernetics) in 1994. Candidate in Physics and Mathematics since 2004. Senior researcher of the Institute of Mathematical Problems of Biology (Branch of the Keldysh Institute of Applied Mathematics, Russian Academy of Sciences). Scientific interests: spectral-analytical methods, algorithms of bioinformatics. Author of more than 20 papers in scientific journals.
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Tetuev Ruslan Kurmanbievich. Born in 1976. Graduated from the Kh.M. Berbekov Kabardino-Balkarian State University in 1998, speciality Applied Mathematics. Received candidate’s degree in Physics and Mathematics at the A.A. Dorodnitsyn Computational Center (Russian Academy of Sciences) by speciality 05.13.17 “Theoretical Foundations of Informatics” in 2007. Scientific interests: algebra of spectral transforms, theoretical informatics. Author of more than 50 papers in Russian and foreign languages in various peer-reviewed journals.
Translated by E. Glushachenkova

Abstract

The generalized spectral-analytical method as a new approach to the processing of information arrays is stated. Some theoretical foundations of this method and its applications in different experimental data analysis problems are given. The method is based on the adaptive expansion of initial arrays in the functional bases belonging to the classical algebraic systems of polynomials and functions of continuous and discrete arguments (Jacobi, Chebyshev, Lagrange, Laguerre, Kravchuk, Charlier, and other polynomials). This approach combines analytical and digital data-processing procedures, thus providing a basis for the universal combined technology for the processing of information arrays. An appreciable part of this review is devoted to video data analysis and pattern-recognition problems. In addition, some relevant applications of this method in biomedical and bioinformation data analysis, recognition, classification, and diagnosis problems are described.

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