[opendtv] Re: 20060117 Mark's (Almost) Monday Memo

  • From: "Albert Manfredi" <bert22306@xxxxxxxxxxx>
  • To: opendtv@xxxxxxxxxxxxx
  • Date: Sat, 21 Jan 2006 17:23:43 -0500

Craig Birkmaier wrote:

>Shannon can help us predict the highest frequency that
>can be represented (without aliasing) for any given raster
>size. So in theory we could create some diabolical image
>that totally saturates the spectra that can be represented
>in a single frame.

I believe you are referring to the Nyquist limit here. That
does apply to images, of course. But Shannon's Law refers
to the limiting bit rate that can be transferred in a given
channel width, as a function of signal to noise ratio. The
analogous limit in image compression might be stated as
"given the pixel count, frequency content, color content, of
a given image, what is the smallest file size that can be
achieved, in theory (i.e. not restricted to any existing
algorithm), with no loss of image information?

>But this is just for one frame. Shannon tells us noting
>about the next frame, except that it can contain no
>more information than the previous "diabolical" frame.

This different form of Shannon's law would be repeated
for all frames in the moving image sequence, in principle,
and information content change would then become a
factor too.

>But the next frame can be equally challenging, but
>totally different. From a compression perspective this
>is truly diabolical - that is there is no relationship from
>one frame to the next, thus very little opportunity to
>take advantage of interframe entropy coding.

Yes, I think this does relate. If you remember the results
of the 4th and 5th gen 8-VSB equalizers, there were
examples where they beat the 14.9 dB C/N for solid
reception. Not that 14.9 is any sort of Shannon limit,
it's not, but the message was that if the "noise" is
somehow correlated to the signal, it can be used to
enhance reception. The Shannon limit is not violated,
though. Because when it appears as if the Shannon liimit
might have been exceeded, it turns out that some of
that "noise" was actually signal, as in S/(N+I).

On the other hand, if the noise is gaussian, i.e.
uncorrelated, then it cannot be used to enhance
reception. So I agree that whatever this new law looked
like, it would have to take into account how much
information change occurred between frames, when it
was applied to moving images. Analogous concepts here.

>In other words, there is no correct answer to Bert's
>question. Any limits will change dynamically based on
>the ability of the compression algorithm to deal with
>specific types of image pathology.

John Shutt's question, actually. I don't know that
anyone has come up with any sort of Shannonesque
law to answer John's question, but I would be surprised
if such a law were undevelopable(?). Again, the answer
would not be related to any one compression algorithm.

And I agree that we are most likely nowhere close to
the limit, with existing algorithms. But that's only a
wild*ss guess.


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