It kind of reads like you have discredited frequency domain compression algorithms. FYI JPEG used a block-based DCT which is very similar to a Fourier transform.
Heck, I've been 17 when I did that. I certainly didn't really know much about the theory behind or why it almost certainly would fail. But I guess by now I wouldn't even attempt such craziness, so in a way it's probably a good thing to not know things too well, sometimes.