Analytical solution and computer simulation of the task of Rician distribution’s parameters in limiting cases of large and small values of signal-to-noise ratio

Yakovleva T.V.
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The paper provides a solution of a task of calculating the parameters of a Rician distributed signal on the basis of the maximum likelihood principle in limiting cases of large and small values of the signal-tonoise ratio. The analytical formulas are obtained for the solution of the maximum likelihood equations’ system for the required signal and noise parameters for both the one-parameter approximation, when only one parameter is being calculated on the assumption that the second one is known a-priori, and for the two-parameter task, when both parameters are a-priori unknown. The direct calculation of required signal and noise parameters by formulas allows escaping the necessity of time resource consuming numerical solving the nonlinear equations’ s system and thus optimizing the duration of computer processing of signals and images. There are presented the results of computer simulation of a task confirming the theoretical conclusions. The task is meaningful for the purposes of Rician data processing, in particular, magnetic-resonance visualization.

Keywords: probability density function, Rice distribution, maximum likelihood method, samples of measurements, signal-to-noise ratio
Citation in English: Yakovleva T.V. Analytical solution and computer simulation of the task of Rician distribution’s parameters in limiting cases of large and small values of signal-to-noise ratio // Computer Research and Modeling, 2015, vol. 7, no. 2, pp. 227-242
Citation in English: Yakovleva T.V. Analytical solution and computer simulation of the task of Rician distribution’s parameters in limiting cases of large and small values of signal-to-noise ratio // Computer Research and Modeling, 2015, vol. 7, no. 2, pp. 227-242
DOI: 10.20537/2076-7633-2015-7-2-227-242
URL: http://crm-en.ics.org.ru/journal/article/2259/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.
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