Wavelet shrinkage for modeling time series data : a data compression method

Abstract

This thesis is my final project report that has been executed at Research and Development section, department of Distribution, Amsterdam Water Supply on from January until June 1999. The aim of this research project is designing a data compression scheme that is suitable for cbd data in general sense, through a modeling process. The compressed data must be contained small numbers of parameters (compare to the original data) and it can be reconstructed to original data (with high quality of approximation). The original data is compressed by transforming into wavelet coefficients in the wavelet domain via Discrete Wavelet Transform (DWT). Because the value of most of the wavelet coefficients are close to zero, so a cutting method is done using three thresholding techniques viz., hard, soft, and SURE that yield wavelet shrinkage coefficients. Wavelet shrinkage coefficients will be stored as a representation of the original data. The proportion of the number of non-zero parameters of the wavelet shrinkage and the number of original date is used as a compression quality measure. The compressed data are reconstructed by transforming the wavelet shrinkage coefficients back to the original domain through Inverse Discrete Wavelet Transform (IDWT). The difference between approximation data and original data is used as approximation quality measure. The cutting method becomes essential in this problem; that's way the research is focused on how to design the cutting procedure. Three scenarios have been designed viz., scenario that emphasis on the compression, approximation and compromise between both compression and approximation. Six data sets are chosen as representations of cbd data; scenario 3 gives the best results 7.4% parameter and 99.12% for quality.