Wavelet denoising of Gaussian peaks: A comparative study

In this paper we apply some recent results on non-linear wavelet analysis to simulated noisy signals of chemical interest. In particular, we compare the wavelet soft universal thresholding algorithm described by Donoho, to Fourier filters and to polynomial smoothers such as the Savitzky-Golay filters (SG). All reconstruction filters were evaluated on the basis of three different criteria: the mean squared error (MSE) both for the whole signal and for an interval centred around the peak, the signal-to-noise ratio (SNR) improvement and the change in the peak area. The simulated data consists of narrow Gaussian peaks with white noise. Signals with low SNR were investigated, since this is a challenging problem for each reconstruction filter. Four common wavelets (Haar, Daubechies, Symmlets and Coiflets) were selected for the wavelet denoising. Our results show that under the chosen conditions wavelet denoising (WD) gives in most cases superior performance over classical filter techniques.