[WM]: DCT energy compression

[Kieran Larkin <kieran.larkin@cisra.canon.com.au>]

A colleague has asked me to pass on the following reply:

There are actually several types of DCT, the most common of which is the
DCT-II (DCT type 2 - but is usually just called the DCT). It is an
approximation to the Karhunen-Loeve transform (KLT - a principle
component type transform) for highly correlated sources - that is
sources whose neighbouring samples are likely to have similar values. In
fact I believe the DCT was developed in an attempt to approximate the
KLT for some (a highly corrleated?) source. Images are the best example
of a highly correlated sources, while audio, I believe, is generally
somewhat less correlated. The fact that JPEG uses the DCT(II) is "a
large body of experimental" evidence of the PCA effectiveness of the DCT
(for images). And despite what some wavelet people will tell you, the
DCT is not really inferior to the discrete wavelet transform in terms of
its PCA ability (for natural images under normal operation conditions).
I guess the fact that audio compressors often use some sort of
overlapping transform means that the DCT is not totally optimum for
audio, but I am out of my area of expertise here. The book "Discrete
cosine
transform: algorithms, advantages and applications" by Rao and Yip has
some details of the PCA like behaviour of the DCT, and although I
haven't read it I believe the paper "Diagonalizing properties of the
discrete cosine transforms" IEEE Trans. Signal Processing, Vol. 43,
pp2631-2641, 1995, discusses a whole class of sources for which the DCT
is optimum.

I hope this is of some help,

Kieran


>Hello watermarkers,
>
>
>I've read in everal papers that the Discrete Cosine Transform has an 
>energy ( defined as the variance, as in Principle Components Analysis) 
>compaction
>
>
>property, and as such is a good approximation of PCA decomposition. 
>Though I have never seen this asumption been denied while experimenting

>on audio signals, I'd like to know if there is a theoretical proof of 
>this, or
>any large experimental result which would give a little justification
to
>this. Thanks in advance




______________________________________________________________________________

Watermarking Mailing List - http://www.watermarkingworld.org/ml.html
To unsubscribe send email to "majordomo@watermarkingworld.org" with
"unsubscribe watermarking YOURMAIL" in the body.
______________________________________________________________________________