Method of Constructing a Nonlinear Approximating Scheme of a Complex Signal: Application Pattern Recognition

Oksana Mandrikova, Bogdana Mandrikova and Anastasia Rodomanskay
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Oksana Mandrikova: Institute of Cosmophysical Research and Radio Wave Propagation, Far Eastern Branch of the Russian Academy of Sciences, Mirnaya st, 7, Paratunka, 684034 Kamchatskiy Kray, Russia
Bogdana Mandrikova: Institute of Cosmophysical Research and Radio Wave Propagation, Far Eastern Branch of the Russian Academy of Sciences, Mirnaya st, 7, Paratunka, 684034 Kamchatskiy Kray, Russia
Anastasia Rodomanskay: Institute of Cosmophysical Research and Radio Wave Propagation, Far Eastern Branch of the Russian Academy of Sciences, Mirnaya st, 7, Paratunka, 684034 Kamchatskiy Kray, Russia

Mathematics, 2021, vol. 9, issue 7, 1-15

Abstract: A method for identification of structures of a complex signal and noise suppression based on nonlinear approximating schemes is proposed. When we do not know the probability distribution of a signal, the problem of identifying its structures can be solved by constructing adaptive approximating schemes in an orthonormal basis. The mapping is constructed by applying threshold functions, the parameters of which for noisy data are estimated to minimize the risk. In the absence of a priori information about the useful signal and the presence of a high noise level, the use of the optimal threshold is ineffective. The paper introduces an adaptive threshold, which is assessed on the basis of the posterior risk. Application of the method to natural data has confirmed its effectiveness.

Keywords: data analysis; nonlinear approximation; wavelet packets; cosmic ray variations; geomagnetic data (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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