Abstract:
The purpose of this thesis is to apply the wavelet transform WT to
multiresolution structures for analyzing the information content of images based on
multiresolution signal decomposition of the wavelet representation. The advantage
of the wavelet transform is the fact that it uses different building blocks than the
Fourier's sines and cosines and can also work around any gaps in the data. The
wavelet block has start and end points and is a right tool for analyzing
nonstationary signals. The wavelet transform is related to wavelets, a scaling
function and an input signal. From Haar scaling and wavelets, the wavelet
transform system was built by using multiresolution signal decomposition. Since
Daubechies' scaling and wavelets contain very unique characteristics, which can
compress signals having constant or linear components, they were chosen to build
both 1-D and 2-D wavelet transforms.
In this thesis, three test signals were carefully selected to be used for
comparing the efficiencies of data compression between the wavelet and the
Fourier transform. By visually inspecting the results, a wavelet reconstructed signal
shows better resolution than the same Fourier reconstructed signal under the
same compression ratio.
The process of signal decomposition and reconstruction is described as
follows: A signal is first broken down into its low and high frequency components.
The part that contains the low frequency components contains most of the
information, is again decomposed into low and high parts. The coarsest signal is
kept in the last stage of the lowpass filter operation. It is obtained through a
pyramidal algorithm based on convolutions with quadrature mirror filters.
Finally, two specific applications (scaling up and image classification) of
wavelet analysis are presented for the case of forested landscapes in the Pacific
Northwest, U.S.A. The NMSE (normalized mean square error) is used to quantify
the amount of information change with image scaling up. To relate changes in
ecological function with changes in ecological pattern and information content
which occurs in the process of data compression using the wavelet, a simple
classification is performed. Thus, changes in information which occur in scaling-up
(i.e. the change in forest pattern which results from filtering using the wavelet) are
related to changes in ecological function.
It is hoped that the results of the study will contribute to issues concerning
data compression using satellite imagery to monitor forest health and develop
understanding for scaling problems in ecology.
