Digital BW, The Print

Roger Howard writes:

> No - assuming no loss, there are real limits to how far compression can
> take you. It's closely related to Shannon's Law.

Yes, but we aren't hitting those limits, because practical compression
algorithms can't do optimal compression.

For example, many modern algorithms do Walsh-Fourier transformations to
compress data.  For practical reasons, these do these only on tiny
chunks of image data at a time; but it's possible to do a single
transformation on the _entire image_.  This latter transformation
results in much better compression ... but it takes an extremely long
time to complete.  And so nobody actually does it.

Exactly how much of a gain this represents, I don't know, because nobody
actually does it.

> Today, the best compressors for really great efficiency on really high
> rez materials tends to be wavelets... JPEG2000 and MrSid are both 
> popular implementations. The artifacts are much less obnoxious than 
> DCT, and the compression ratios are much better. For really large 
> images, unless you regularly view them at 100% then a wavelet 
> compressor (or even DCT) can be used pretty heavily without losing too
> much significant detail.

If you keep the frequencies high enough, you should be able to get
effectively lossless compression.  The frequencies would have to be
infinitely high to get perfect lossless compression, though (if I'm not
mistaken).

In any case, as I've said, I think the future is in more bandwidth and
more storage space, not greater compression.  As you point out yourself,
Shannon proved that one can only do so much with (lossless--meaning
perfectly reversible) compression.