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Today there was a talk about wavelets in our colloquium. I took a course on signal processing and wavelets a few years ago – so this wasn't exactly news for me. Indeed I was by far not impressed by the talk as it neither offered new insights nor made the important parts of using the wavelet transform clear. Add to that that only the discrete case was treated and I'm a bit annoyed.
He mentioned that JPEG 2000 uses wavelet compression. So I gave it a quick test run – seeing that both GraphicConverter and QuickTime and thus (?) Safari are happy to deal with JPEG 2000 files. Just compare the files presented here. The top one is exciting new JPEG 2000, the bottom one boring old FFT JPEG. Files are about the same size in both cases...
Riight, skip that. I'll prepare the images tomorrow as GraphicConverter's file size estimates weren't quite right and I don't have the time to re-do everything right now.
The point I want to make is the following: While Wavelet compression is supposed to be much better than JPEG in the examples shown by Wavelet promoters – all I've seen in practice are rather tiny advantages in size, far off from what the demos suggest. Why is that? Are the making this up? Are they using highly optimised wavelets for their examples? (I've seen for myself that the choice of wavelet used for compression can make a huge difference.) Are the JPEG 2000 algorithms that make it to the general public not quite well done yet?
Discuss.