LINEAR DIMENSION REDUCTION OF SEQUENCES OF MEDICAL IMAGES .2. DIRECT SUM DECOMPOSITION

Using unitary transformations together with a previously described sta tistical theory for optimal linear dimension reduction it is shown how pixels in a sequence of images can be decomposed into a sum of variat es, covariates, and residual vectors, with all covariances equal to ze ro. It is demonstrated that this decomposition is optimal with respect to noise. In addition, it results in simplified and well conditioned equations for dimension reduction and elimination of covariates. The f actor images are not degraded by subdivision of the time intervals. In contrast to traditional factor analysis, the factors can be measured directly or calculated based on physiological models. This procedure n ot only solves the rotation problem associated with factor analysis, b ut also eliminates the need for calculation of the principal component s altogether. Examples are given of factor images of the heart, genera ted from a dynamic study using oxygen-15-labelled water and positron e mission tomography. As a special application of the method, it is show n that the factor images may reveal any contamination of the blood cur ve derived from the original dynamic images with myocardial activity.