It lets you edit only items around certain detail sizes - often called 'detail levels'.
Here's a moonshot after post-processing:
Some might say it looks OK but I wanted more acutance:
I increased the contrast in Levels 1, 2, 3 ... 1px,2px,4px detail size, voila:
Thing with wavelets is that one can do anything to individual levels - like change the color of grass to orange and sky to purple ... or smooth a background without smoothing fine details. And more ...
... patdavid.net/2014/07/wavelet-decompose-again/
Hope this is of interest ...