Multiresolution Signal Decomposition PDF Download

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.