Databases Reference
In-Depth Information
15
Wavelets
15.1 Overview
In this chapter, we introduce the concept of wavelets and describe how to use
wavelet-based decompositions in compression schemes. We begin with an in-
troduction to wavelets and multiresolution analysis and then describe how we
can implement a wavelet decomposition using filters. We then examine the
implementations of several wavelet-based compression schemes.
15.2 Introduction
In the previous two chapters, we looked at a number of ways to decompose a signal. In this
chapter, we look at another approach to decompose a signal that has become increasingly
popular: the use of wavelets. Wavelets are being used in a number of different applications.
Depending on the application, different aspects of wavelets can be emphasized. As our particu-
lar application is compression, we will emphasize those aspects of wavelets that are important
in the design of compression algorithms. You should be aware that there is much more to
wavelets than is presented in this chapter. At the end of the chapter we suggest options if you
want to delve more deeply into this subject.
The practical implementation of wavelet compression schemes is very similar to that of
subband coding schemes. As in the case of subband coding, we decompose the signal using
analysis filter banks. The outputs of the filter banks are downsampled, quantized, and encoded.
The decoder decodes the coded representations, upsamples, and recomposes the signal using
a synthesis filter bank.
