Intuitively, wavelets, and SP in general, seem like something behavioral folks could benefit from, but I can't come up with any good use cases that would justify going through all the associated math.
Yeah, I agree. Wavelets were all the rage in the late 80's and 90's and they seem to have fallen out of fashion.
As a matter of fact, It's kind of strange that applied math techniques be subject to fashion.
I think there is quite a lot to be done looking at deep nets in terms of wavelets for example.
Apropos deep nets, with the explosion in machine learning in the past few years, I've been seeing a lot of research interest statements change to meet that. In particular, there's an awful lot of numerical linear algebra being done now.
I suspect that things will come full-circle soon enough, and those tools developed in numerical linear algebra (via their connections to functional analysis) will make their way to harmonic analysis.
(This is notwithstanding the fact that compressed sensing is picking up a little momentum as a research area in applied mathematics and other disciplines that study signal processing. Wavelets, curvelets, shearlets, chirplets, etc. will likely see some action there too.)
I suspect the OP is not talking about how deep nets are implemented, but rather how people are trying to understand how and why they work so well, or how to reverse-engineer knowledge out of a trained net, or how to train them faster, etc ...
In that space, you need quite a bit more than matrix multiplication.