The Karhunen-Loeve transform for incomplete data

R.M. Everson and L. Sirovich

Abstract

This paper addresses the problem of using the Karhunen-Loeve transform with partial data. Given a set of empirical eigenfunctions we show how to recover the modal coefficients for each gappy snapshot by a least-squares procedure. This method gives an unbiased estimate of the data that lay in the gaps and permits gaps to be filled in a reasonable manner. In addition, a scheme is advanced for finding empirical eigenfunctions from gappy data. It is shown numerically that this obtains spectra and eigenfunctions that are close to those obtained from unmarred data.

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