Abstract:
The paper provides a solution of the two-parameter task of joint signal and noise estimation at data analysis within the conditions of the Rice distribution by the techniques of mathematical statistics: the maximum likelihood method and the variants of the method of moments. The considered variants of the method of moments include the following techniques: the joint signal and noise estimation on the basis of measuring the 2-nd and the 4-th moments (MM24) and on the basis of measuring the 1-st and the 2-nd moments (MM12). For each of the elaborated methods the explicit equations' systems have been obtained for required parameters of the signal and noise. An important mathematical result of the investigation consists in the fact that the solution of the system of two nonlinear equations with two variables - the sought for signal and noise parameters - has been reduced to the solution of just one equation with one unknown quantity what is important from the view point of both the theoretical investigation of the proposed technique and its practical application, providing the possibility of essential decreasing the calculating resources required for the technique's realization. The implemented theoretical analysis has resulted in an important practical conclusion: solving the two-parameter task does not lead to the increase of required numerical resources if compared with the one-parameter approximation. The task is meaningful for the purposes of the rician data processing, in particular - the image processing in the systems of magnetic-resonance visualization. The theoretical conclusions have been confirmed by the results of the numerical experiment.
Keywords:
probability density function, Rice distribution, likelihood function, maximum likelihood method, method of moments, signal to noise ratio, noise dispersion.
Citation:
T. V. Yakovleva, “Theoretical substantiation of the mathematical techniques for joint signal and noise estimation at rician data analysis”, Computer Research and Modeling, 8:3 (2016), 445–473
\Bibitem{Yak16}
\by T.~V.~Yakovleva
\paper Theoretical substantiation of the mathematical techniques for joint signal and noise estimation at rician data analysis
\jour Computer Research and Modeling
\yr 2016
\vol 8
\issue 3
\pages 445--473
\mathnet{http://mi.mathnet.ru/crm3}
\crossref{https://doi.org/10.20537/2076-7633-2016-8-3-445-473}
Linking options:
https://www.mathnet.ru/eng/crm3
https://www.mathnet.ru/eng/crm/v8/i3/p445
This publication is cited in the following 4 articles:
T. V. Yakovleva, N. S. Kulberg, D. V. Leonov, “Estimation of the size of structural formations in ultrasound imaging through statistical analysis of the echo signal”, Dokl. Math., 107:1 (2023), 72–76
T. V. Yakovleva, “Svoistvo ustoichivosti statisticheskogo raspredeleniya Raisa: teoriya i primenenie v zadachakh izmereniya fazovogo sdviga signalov”, Kompyuternye issledovaniya i modelirovanie, 12:3 (2020), 475–485
T. V. Yakovleva, “Raschet signala i shuma pri analize raisovskikh dannykh putem kombinirovaniya metoda maksimuma pravdopodobiya i metoda momentov”, Kompyuternye issledovaniya i modelirovanie, 10:4 (2018), 511–523
T. V. Yakovleva, “Opredelenie parametrov signala i shuma pri analize raisovskikh dannykh metodom momentov nizshikh nechetnykh poryadkov”, Kompyuternye issledovaniya i modelirovanie, 9:5 (2017), 717–728
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