Some methods of solving inverse incorrect problems in a physical experiment

D. Z. Galimullin, M. E. Sibgatullin, D. I. Kamalova, M. Kh. Salakhov

Institute of Physics, Kazan (Volga region) Federal University

Abstract: In this paper, some mathematical methods for processing and interpreting data obtained from a physical experiment are considered. These methods have been developed at the Department of Optics and Nanophotonics of Kazan Federal University. They are based on the use of knowledge about signal structure fractal characteristics, neural network, wavelet transform analysis and wavelet-based derivative spectrometry, genetic algorithms, and wavelet bispectra. The methods under study are suitable for solving many inverse incorrect problems of a physical experiment.

Keywords: wavelet transform analysis, statistics of higher orders, neural networks, wavelet-based derivative spectrometry, evolutionary algorithms, fractal characteristics, colored noise.

UDC: 53.087/.088

Received: 13.05.2010