Signal smoothing

Once all the spectra have had their baseline corrected and been translated into the same range of intensities, the next processing step is to smooth the signal wavefrom the input signal. As mentioned before, the original signal is always perturbed by different noises $\varepsilon (t)$ supposedly coming from the detection instruments. Nevertheless, this preprocessing step has not always been tackled independently, as some authors prefer to combine the smoothing step with some of the other preprocessing stages, e.g. with normalization [13].

The main idea of signal smoothing is to avoid the low signal fluctuations. A great many false-positive peaks are likely to be found if the signal has not been previously smoothed and all the low resolution peaks removed. Therefore, this step should be taken before any peak detection algorithm is used. Even after applying noise reduction, we cannot rule out some of the detected peaks being due to noise perturbations, although this is minimized.

The most common signal smoothing technique is wavelet denoising proposed by [6,5]. It makes use of the undecimated wavelet transformation to estimate the wavelet coefficients. These are then used to denoise the signal and obtain a smoothed signal. There exists an online library, namely the Cromwell package, that includes all the denoising and smoothing functions. Figure 1 presents a small portion of the $m/z$ axis of one illustrative spectrum.

Figure 1: Graphical example of the first preprocessing tasks in our proposed pipeline: baseline removal, normalization and wave smoothing. The thin solid line plots the observed relative intensity in a segment of the $m/z$ axis. The other lines show how the original data is corrected in each of the three preprocessing stages.