I want especially to pay your attention on the fact, that K-L transform - is an adaptive technique of Signal Processing. It means, that you obtain (construct) the basis for signal or image decomposition just from the data set (signal or image) without using any other functions. It's a very important property, because it helps take into account local properties and internal structure of the process.
Also, among the other adaptive technique, it's worth mentioning the following:
1) Empirical Mode decomposition
2) Singular spectrum analysis
3) Wavelet transform
With respect,
Dmitrij