  This paper describes a fast and accurate method for obtaining steerable
principal components from a large dataset of images, assuming the images are
well localized in space and frequency. The obtained steerable principal
components are optimal for expanding the images in the dataset and all of their
rotations. The method relies upon first expanding the images using a series of
two-dimensional Prolate Spheroidal Wave Functions (PSWFs), where the expansion
coefficients are evaluated using a specially designed numerical integration
scheme. Then, the expansion coefficients are used to construct a
rotationally-invariant covariance matrix which admits a block-diagonal
structure, and the eigen-decomposition of its blocks provides us with the
desired steerable principal components. The proposed method is shown to be
faster then existing methods, while providing appropriate error bounds which
guarantee its accuracy.
