The Karhunen-Loeve transform for incomplete data

Abstract

This paper addresses the problem of using theKarhunen-Loeve transform with partial data. Given aset of empirical eigenfunctions we show how torecover the modal coefficients for each gappysnapshot by a least-squares procedure. This methodgives an unbiased estimate of the data that lay inthe gaps and permits gaps to be filled in areasonable manner. In addition, a scheme isadvanced for finding empirical eigenfunctions fromgappy data. It is shown numerically that thisobtains spectra and eigenfunctions that are close tothose obtained from unmarred data.