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 (L2 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 L2 approximations.
© 1999 Optical Society of America
(110.6980) Imaging systems : Transforms
Original Manuscript: March 30, 1998
Revised Manuscript: September 8, 1998
Manuscript Accepted: September 17, 1998
Published: January 1, 1999
A. Levy and J. Rubinstein, "Hilbert-space Karhunen–Loève transform with application to image analysis," J. Opt. Soc. Am. A 16, 28-35 (1999)