Statistical distribution of factors and factor images in factor analysis of medical image sequences

From a time or energy image sequence, factor analysis of medical image sequences (FAMIS) estimates factors, representing kinetics or spectra in a given physiological compartment, and associated factor images, showing the compartments corresponding to each curve. In this paper, we show that the statistical properties of factor images and associated factors can be determined using a well known result from elementary probability theory. Numerical experiments are conducted to demonstrate that the variance observed in factor images can be predicted when the statistical properties of the original data are known. It is shown how these theoretical results can be used to relax the non-negativity constraints during FAMIS oblique analysis and to improve the quantitative interpretation of the factor images by associating a confidence interval with each pixel value.