Two-stage iteratively reweighted smoothing splines for baseline correction

This paper reviewed several iteratively reweighted baseline correction methods. We note in the literature that the estimated baselines are susceptible to random noises in a low signal-to-noise signal. When the acquired signals are complex-structured, the estimated baselines may still contain the peak information. This paper proposes a new approach named two-stage iteratively reweighted smoothing splines (RWSS) to cope with those situations. The proposed method estimates the baselines by applying weighted smoothing splines in two stages. The first stage applies the smoothing splines with Tukey's Bisquare weights to estimate the baselines, while the second stage is designed to fine-tune the first stage's result. Specifically, the weighted smoothing splines are applied again to remove the remaining peak information, where the weights for the peak regions are inversely proportional to the error variances. By simulation studies, the performance of the two-stage RWSS algorithm is among the best in terms of the root mean square error. Finally, we conducted three real data studies, i.e., chromatograms, infrared spectra, and Raman spectra, to verify the reliability of our new algorithm in practical tasks by evaluating principal components and classification accuracy. The new algorithm is implemented in R language, where the source code is available at https://github.com/rwss2021/rwss.