Databases Reference
In-Depth Information
Source
encoder
Source
X
X
c
Channel
Source
decoder
User
Y
X
c
F I GU R E 8 . 2
Block diagram of a generic compression scheme.
talk about “as few bits as possible," and “close approximation," and in the following sections
we will introduce quantitative measures that will allow us to be more precise in our language.
is generally highly correlated, with significant de-
pendencies between samples. However, for many of the theoretical results we will assume
that the sequence can be modeled as independent identically distributed random variables.
Surprisingly, even with this gross level of simplification we can obtain results that provide
significant insight into the source coding process. For these theoretical developments we will
use the block diagram and notation shown in Figure
8.2
. The output of the source is modeled as
a random variable
X
.The
source coder
takes the source output and produces the compressed
representation
X
c
. The channel block represents all transformations the compressed represen-
tation undergoes before the source is reconstructed. We will take the channel to be the identity
mapping, which means
X
c
=
X
c
. The source decoder takes the compressed representation
and produces a reconstruction of the source output for the user.
In the following sectionwewill examine themore popularmeasures of fidelity, or closeness,
between the information sequence
The information-bearing sequence
{
x
n
}
{
x
n
}
and the reconstructed sequence
{
y
n
}
.
8.3 Distortion Criteria
How do we measure the closeness or fidelity of a reconstructed source sequence to the original?
The answer frequently depends on what is being compressed and who is doing the answering.
Suppose we were to compress and then reconstruct an image. If the image is a work of art
and the resulting reconstruction is to be part of a topic on art, the best way to find out how
much distortion was introduced and in what manner is to ask a person familiar with the work
to look at the image and provide an opinion. If the image is that of a house and is to be used
in an advertisement, the best way to evaluate the quality of the reconstruction is probably to
ask a real estate agent. However, if the image is from a satellite and is to be processed by
a machine to obtain information about the objects in the image, the best measure of fidelity
is to see how the distortion introduced affects the functioning of the machine. Similarly, if
we were to compress and then reconstruct an audio segment, the judgment of how close the
reconstructed sequence is to the original depends on the type of material being examined as
well as the manner in which the judging is done. An audiophile is much more likely to perceive
