Statistical analysis of MR imaging and its applications in image modeling

This paper presents a statistical description of MR imaging, from the imaging equation to the image random field. Both thermal noise and object variability are considered in the pixel images generated by Fourier transform reconstruction algorithm. The Gaussianity, stationarity, dependence and ergodicity of MR image random field are characterized as the standard problems of statistics, and justified to form the basis for establishing the stochastic image model and conducting the statistical image analysis. An application of these properties to the finite normal mixture modeling of MR images is demonstrated, and a new mathematical understanding is discussed based on some new findings