Computer Research and Modeling, 2015 Volume 7, Issue 2,Pages 227–242(Mi crm182)
MATHEMATICAL MODELING AND NUMERICAL SIMULATION
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
Abstract:
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-to-noise 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.
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