[Mp4-tech] Why only low frequeny is considered in DCT?

[Gary Sullivan]

I want to further clarify my statement saying "So when we use the pdf of
the quantized transform coefficients to perform entropy coding of their
values, they compress rather well since many of them tend to be equal to
0 most of the time."
To be more precise, they compress rather well since the pdf of the
quantized transform coefficients is a highly non-uniform distribution
and also since the variance of the transform coefficients for high
frequencies is much smaller than the variance of the transform
coefficients for low frequencies.  It is not just a matter of zero
values versus non-zero values.  In fact there is nothing special about
the zero value.  It is just one of the values in the pdf and it is only
particularly interesting because it is the most common value.  What
matters most is that 1) small values are much more likely to occur than
large values, and 2) low frequencies are much more likely to have large
amplitudes than high frequencies.
For a more proper understanding, read Jayant & Noll or Huang &
Schultheiss or similar stuff.
Perhaps I should also correct my poorly-written typing of the phrase
"poorly-written".  :-)
Best Regards,
Gary Sullivan
________________________________
	From: mp4-tech-bounces lists.mpegif.org
[mailto:mp4-tech-bounces lists.mpegif.org] On Behalf Of Gary Sullivan
	Sent: Thursday, November 23, 2023 2:16 AM
	To: sagar; mp4-tech lists.mpegif.org
	Subject: RE: [Mp4-tech] Why only low frequeny is considered in
DCT?
	Sagar et al,
	It sounds like you have been reading some pooly-written
tutorial(s) about how DCT coding works.  I have seen some pretty bad
descriptions of the concepts of DCT coding.  (Hopefully, you won't
respond by saying you learned what you know by reading my papers on the
subject. :-)  One important thing to keep in mind is the difference
between what we expect will happen most of the time and what might
possibly occur on some specific set of worst-case input data.
	Actually, when we use DCT coding (e.g., for ordinary JPEG 1
still-image coding), we ordinarily *do* consider *all* frequency
components.  We transform each block of data and quantize the resulting
frequency-domain coefficients - that includes quantization of both the
low-frequency and high-frequency components.  All of them.
	Usually that quantization process involves the application of
what is known as a "mid-tread" scalar quantizer.  In other words, the
quantizer is structured such that one of the selectable output
reconstruction values is exactly equal to 0.  See, for example, the book
by Jayant and Noll for some discussion of such quantizers.
	Actually you can still perform effective data compression even
if you use a "mid-rise" quantizer and it will still function just fine
for high bit rate coding.  But such a design would have difficulty
operating at low bit rates, since a mid-rise quantizer tends to have an
output entropy exceeding one bit per sample.
	Anyhow, what happens is that for image and video coding at
relatively low bit rates, we can observe that when we apply a mid-tread
scalar quantizer to the transform coefficients, we observe that many of
the high-frequency components usually end up with a quantized value of
0.  That doesn't mean that we force them to be zero.  It just means that
this is what tends to happen most of the time.
	So when we use the pdf of the quantized transform coefficients
to perform entropy coding of their values, they compress rather well
since many of them tend to be equal to 0 most of the time.
	This is a consequence of the cross-correlation properties of
image and video data.  Such data tends to contain more low-frequency
content than high-frequency content most of the time.  Another way to
express that is to say that the input data tends to be highly
correlated.
	But the coding technology design does not force that.  If you
feed a low-correlation input image to a good JPEG coder, it will still
be able to represent the image (although it might require more bits to
code with reasonable fidelity than a smoother image would).
	If you want to really understand this stuff, study up on what a
KLT is, and perhaps read some things like the book by Jayant and Noll
and perhaps the paper by Huang and Shultheiss and perhaps the original
papers and books by Rao et al on the development of the DCT.  There are
probably also lots of other places where such things are described well.
	Best Regards,
	Gary Sullivan
________________________________
		From: mp4-tech-bounces lists.mpegif.org
[mailto:mp4-tech-bounces lists.mpegif.org] On Behalf Of sagar
		Sent: Wednesday, November 22, 2023 9:26 PM
		To: mp4-tech lists.mpegif.org
		Subject: [Mp4-tech] Why only low frequeny is considered
in DCT?
		Hi Xperts,
		I wanted to know when we do DCT ( video preocessing), we
only consider the Low frequency elements. Why? 
		DCT is used for taking out spatial reduncies, and DCT is
basically used to decorrelate energy in the image.
		And other fact being low frequency contains high energy,
		If anybody could answer my question, i would be
thankful.
		Warm Regards,
		Sagar
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