> Can a wavelet be used with SIMD 128bit operations?

Popcount works great in this context, but that only gives you linear speedups. Doing rank/select in O(1) instead of O(N) is a bigger win, and you get that by precomputing superblocks.

> Or are they used with 4x4 Matrix operators? Are wavelets good for that kind of math?

Nope, different kind of matrix. Just refers to a nicer packing of a wavelet tree with space wasted by bookkeeping pointers between tree nodes.