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

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.