Mathematical statistics methods as a tool of two-parametric magnetic-resonance image analysis

The paper considers the methods of the magnetic-resonance image analysis, based on the solution of the so-called two-parametric task. The elaborated methods provide joint calculation of both statistical parameters — the mathematical expectation of the random value being analyzed and its dispersion, i. e., simultaneous estimation of both the useful signal and the noise. The considered variants of the task solution employ the methods of mathematical statistics: the maximum likelihood method and variants of the method of moments. A significant advantage of the elaborated two-parametric approach consists in the fact that it provides an efficient solution of nonlinear tasks including the tasks of noise suppression in the systems of magnetic-resonance visualization. Estimation of the sought-for parameters is based upon measured samples' data only and is not limited by any a priori suppositions. The paper provides the comparative analysis of the considered methodology's variants and presents the results of the computer simulation providing the statistical characteristics of the estimated parameters' shift and scatter while solving the task by various methods. The presented methods of the Rician signal's two-parametric analysis can be used within new information technologies at the stage of the stochastic values' processing.