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Hilbert-space Karhunen-Loève transform with application to image analysis.

A Levy·J Rubinstein
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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 (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.

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BibTeXRIS

A Levy, J Rubinstein. 1999. Hilbert-space Karhunen-Loève transform with application to image analysis.. https://doi.org/10.1364/josaa.16.000028

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