Given two highly correlated sources, X and Y, with respective entropies
H(X) and H(Y), and joint entropy H(X,Y), the entropy reached by jointly
encoding the two sources is called the joint entropy of the two sources,
denoted by H(X,Y). A surprising fact,
established -at least in theoratical sense- by Slepian and Wolf is that it is
possible to encode the two highly correlated sources, X and Y, separately, and
still reach the joint entropy, H(X,Y), by decoding them at a joint decoder.
[1]
Thus, in a system with two entirely independent encoders, each coding either
X or Y, and a joint decoder, it is possible to reach the same entropy as a
joint encoder/joint decoder system would reach. This theorem, if it can be translated into practice by efficient coding algorithms, may have a significant
impact in image communications because it can lower the complexity of
source coders used in mobile communications by allowing independence between
them. The diagram below illustrates this separate encoding (followed by
joint decoding) of two highly correlated images, known as Distributed
Source Coding. [4]
Figure 1) Distributed Source Coding of Highly Correlated
Sources (figure by S. Pradhan)
 
It should be re-emphasized that the Slepian-Wolf Theorem, which provides the
theoratical basis for achieving H(X,Y) through distributed source coding is
valid for highly correlated sources, which is the only limitation of
a possible Distributed Source Coding algorithm. However, as both the natural
still images and the individual frames in video do have high intra/inter pixel
correlations, the Distributed Source Coding concept is well-suited and
applicable for image and video compression applications.
 
Hence, this project aims to efficiently compress pairs of highly correlated
still images (which are separately encoded and jointly decoded) through
exploiting the inter and intra pixel correlations inherent in these image
pairs. The ultimate goal is to reach the joint entropy, H(X,Y), rate suggested
by Slepian and Wolf. [1]
ABSTRACT
INTRODUCTION
PROBLEM DESCRIPTION and PRIOR WORK
DATA SET
ALGORITHM
RESULTS
CONCLUSIONS
REFERENCES