[jarenmf]

I think one of the major advantages of wavelets is the time-frequency representation of the signal, which means being able to see the different spectra of the signal change over time (at different scales) which is not easily attainable with Fourier transform. So you could detect transient interesting patterns (spatial frequencies) in the data that would otherwise go unnoticed. Same you could enhance or remove certain spatial frequencies of the signal depending on the task.