Efficient calculation of the principal components of imaging data

Abstract

Principal components analysis (PCA) of images is important in many applications such as positron emission tomography and functional magnetic resonance imaging. PCA is difficult for image data because the correlation matrix is very large. We present a direct method of calculating the PCA of the voxels from the small matrix expressing the correlations between images, instead of the larger matrix representing the correlations between voxels. The method is fast and accurate. It is faster and requires less memory than a singular value decomposition, although it is less accurate. It is much faster and more accurate than iterative and other approximate methods developed for this problem.