Peculiarities of the Rice Statistical Distribution: Mathematical Substantiation
Applied and Computational Mathematics
Volume 7, Issue 4, August 2018, Pages: 188-196
Received: Sep. 16, 2018; Published: Sep. 18, 2018
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Tatiana Yakovleva, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Moscow, Russia
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The Rice statistical distribution has recently become a subject of increasing scientific interest due to its wide applicability in various fields of science and technology, such as the magnetic-resonance visualization and ultrasound diagnostics in medicine, the radio and radar signals’ analysis and processing, the optical measurements, etc. The common feature of the tasks that are adequately described by the Rician statistical model consists in the fact that the value to be measured and analyzed is an amplitude, or an envelope of the output signal which is composed as a sum of the initially determined informative component and a random noise component being formed by many independent normally-distributed summands. The efficient reconstruction of the Rician signal’s informative component against the noise background is shown to be achieved only on the basis of joint determination of both a priori unknown Rician parameters. The Rice statistical distribution possesses some peculiarities that allow solving rather complicated tasks connected with the stochastic data processing. The paper considers the issues of the strict mathematical substantiations of the Rice distribution properties that are meaningful for its efficient application, namely: the Rician likelihood function features and the stable character of the Rice distribution. There are provided the rigorous proofs of the mentioned properties.
Rice Distribution, Probability Density, Likelihood Function, Data Processing
To cite this article
Tatiana Yakovleva, Peculiarities of the Rice Statistical Distribution: Mathematical Substantiation, Applied and Computational Mathematics. Vol. 7, No. 4, 2018, pp. 188-196. doi: 10.11648/j.acm.20180704.12
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