Hi everyone, and thanks for the replies. Most wavelet work has seemed to concentrate on the mathematical structures of the wavelets (in one dimension) themselves (for instance, orthogonal vs. continuous, and lifting vs. frames, etc.). I guess this comes from thought about how the Fourier transform applies to higher dimensions. Say, in an image, you transform along the x axis of an image, then the y axis. This is mathematically consistent with a Cartesian arrangement of the data in an image, but a Cartesian arrangement usually has nothing to do with the arrangement of the scene contrast elements contained in an image - the C. arrangement is just a human imposition of structure where it doesn't really exist. Blah, blah (sorry, I know I talk too much). The "separability" comes from the separability of the transform into the x and y (say) coordinates.
Anyway, this result is artifacts - for instance, in a 2D Daub. wavelet transform of a smooth circle, the scene contrast elements at 45 degrees to the pixel coordinate system are "enhanced." The ridgelets and curvelets, as well as things like matching pursuit and entropy treeing are ways to sort of get around these - but they come from the coordinate grid so you sort of cannot get rid of them. Two fixes seem to be buried deep in the literature: (1) creating wavelets of the same dimension as the dataset (2D wavelets for images) - and these wavelets are not simple combinations of 1D wavelets; and (2) performing "tricks" with the underlying grid (at least, that's how I understand it) - the "quincunx" grid transforms rotate and decimate the grid so there's no preferred direction in, say, a 2D transform. I think these two may actually be different aspects of the same thing.
