Abstract

A generalization of the Karhunen–Loève (KL) transform to Hilbert spaces is developed. It allows one to find the best low-dimensional approximation of an ensemble of images with respect to a variety of distance functions other than the traditional mean square error ($L_2$ norm). A simple and intuitive characterization of the family of Hilbert norms in finite-dimensional spaces leads to an algorithm for calculating the Hilbert-KL expansion. KL approximations of ensembles of objects and faces optimized with respect to a norm based on the modulation transfer function of the human visual system are compared with the standard $L_2$ approximations.

© 1999 Optical Society of America

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