Comment by sinwave

Thought I'd chime in that for image compression (e.g in the JPEG2000 standard), the 2D discrete wavelet transform takes advantage of similar pixel intensities for neighboring pixels at various scales (i.e. "transformed magnitudes all nice and grouped for you"). The 2D-DWT is actually pretty cool under the hood. And, asymptotically, a bit faster than the FFT (DWT runs in O(N), and in 2D, O(width*height)).