A fast wavelet-based Karhunen–Loeve transform

摘要

The paper describes the role of the standard wavelet decomposition in computing a fast Karhunen–Loeve transform. The standard wavelet decomposition (which we show is different from the conventional wavelet transform) leads to a highly sparse and simply structured transformed version of the correlation matrix which can be easily subsetted (with little loss of Frobenius norm). The eigenstructure of this smaller matrix can be efficiently computed using standard algorithms such as QL. Finally, we provide an example of the use of the efficient transform by classifying a 219-channel AVIRIS image with respect to its eigensystem.