Applications involve (i) a project on identifying icosahedral twins from a single HREM image in collaboration with Jon Bailey (now at WU) and Max Bertino (Physics UMR), (ii) a project on tracking columnar growth nucleation in Cu2O films on Si with Jay Switzer (Chemistry UMR), and (iii) quite a few projects which involve strain mapping, e.g. in quantum wires, heterostructures, VLSI silicon, metal nanoclusters and aerosol catalysts.
I also think the mathematics is interesting, in part because the digital version of this technique (long exploited in nature) may be an applied area of mathematical interest largely ignored because of it's poor convergence properties in terms of the Balian-Low theorem. If so, it won't be the first time that applications have illuminated new directions in the landscape of wavelet and sister applications, nor the first time that sloppy math inspired by physical science applications has "tunneled inquiry" into obscure areas worthy of a bit more rigor.
Here are some web notes put together on digitial and analog darkfield decomposition strategies, and the applications we are putting them to...
Note: the first link was written before I had a clear idea about the technical meaning of wavelet per se. At that point I was considering it to refer to any decomposition with localization in both direct and frequency space.