Databases Reference
In-Depth Information
Mathematical Preliminaries for
Lossy Coding
8.1 Overview
Before we discussed lossless compression, we presented some of the mathemat-
ical background necessary for understanding and appreciating the compression
schemes that followed. We will try to do the same here for lossy compres-
sion schemes. In lossless compression schemes, rate is the general concern.
With lossy compression schemes, the loss of information associated with such
schemes is also a concern. We will look at different ways of assessing the impact of the loss
of information. We will also briefly revisit the subject of information theory, mainly to get
an understanding of the part of the theory that deals with the trade-offs involved in reducing
the rate, or number of bits per sample, at the expense of the introduction of distortion in the
decoded information. This aspect of information theory is also known as rate distortion the-
ory. We will also look at some of the models used in the development of lossy compression
schemes.
8.2 Introduction
This chapter will provide some mathematical background that is necessary for discussing
lossy compression techniques. Most of the material covered in this chapter is common to
many of the compression techniques described in the later chapters. Material that is spe-
cific to a particular technique is described in the chapter in which the technique is presented.
