| Abstract
| - Discrete wavelet transform (DWT) denoising contains three steps: forward transformation of the signal tothe wavelet domain, reduction of the wavelet coefficients, and inverse transformation to the native domain.Three aspects that should be considered for DWT denoising include selecting the wavelet type, selectingthe threshold, and applying the threshold to the wavelet coefficients. Although there exists an infinite varietyof wavelet transformations, 22 orthonormal wavelet transforms that are typically used, which include Haar,9 daublets, 5 coiflets, and 7 symmlets, were evaluated. Four threshold selection methods have beenstudied: 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, soft,garrote, and firm), level-dependent, data-dependent, translation invariant (TI), and wavelet package transform(WPT) thresholding methods. The different DWT-based denoising methods were evaluated by using syntheticdata containing white Gaussian noise. The results of comparison have shown that most DWTs are verypowerful methods for denoising and that the MDL and the TI methods are practical. The MDL criterion isthe 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 resultswere obtained. Savitzky−Golay and Fourier transform denoising results were used as reference methods.IR and HPLC data were used to compare denoising methods.
|
