DIFFERENT DISCRETE WAVELET TRANSFORMS APPLIED TO DENOISING ANALYTICALDATA

Discrete wavelet transform (DWT) denoising contains three steps: forwa rd transformation of the signal to the wavelet domain, reduction of th e wavelet coefficients; and inverse transformation to the native domai n. Three aspects that should be considered for DWT denoising include s electing the wavelet type, selecting the threshold, and applying the t hreshold to the wavelet coefficients. Although there exists an infinit e variety of wavelet transformations, 22 orthonormal wavelet transform s that are typically used, which include Haar, 9 daublets, 5 coiflets, and 7 symmlets, were evaluated. Four threshold selection methods have been studied: universal, minimax, Stein's unbiased estimate of risk ( SURE), and minimum description length (MDL) criteria. The application of the threshold to the wavelet coefficients includes global (hard, so ft, garrote, and firm), level-dependent, data-dependent, translation i nvariant (TI), and wavelet package transform (WPT) thresholding method s. The different DWT-based denoising methods were evaluated by using s ynthetic data containing white Gaussian noise. The results of comparis on have shown that most DWTs are very powerful methods for denoising a nd that the MDL and the TI methods are practical. The MDL criterion is the only method that can select a threshold-for wavelet coefficients and select an optimal transform type. The TI method is insensitive to the wavelet filter so that for a variety of wavelet filters equivalent results were obtained. Savitzky-Golay and Fourier transform denoising results were used as reference methods. IR and HPLC data were used to compare denoising methods.