MR imaging statistics and its application in image modeling

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Abstract
This paper presents a new framework on a complete statistical description of MR imaging and its application in image modeling. Particular studies include object variability and thermal noise, statistical properties of pixel images, and stochastic regularities of context images. Six stochastic properties (Gaussianity, stationarity, dependence, ergodicity, Markovian property, inhomogeneity) are justified to form the basis for establishing the stochastic image models. The application of these properties to both pixel image modeling (standard finite normal mixture) and context image modeling (Markov random field) is discussed mathematically. The correct use of the statistical models in image analysis is verified in terms of new observations, theorems, and interpretations.

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