Automated Spectral Smoothing with Spatially Adaptive Penalized Least Squares

Abstract

A variety of data smoothing techniques exist to address the issue of noise in spectroscopic data. The vast majority, however, require parameter specification by a knowledgeable user, which is typically accomplished by trial and error. In most situations, optimized parameters represent a compromise between noise reduction and signal preservation. In this work, we demonstrate a nonparametric regression approach to spectral smoothing using a spatially adaptive penalized least squares (SAPLS) approach. An iterative optimization procedure is employed that permits gradual flexibility in the smooth fit when statistically significant trends based on multiscale statistics assuming white Gaussian noise are detected. With an estimate of the noise level in the spectrum the procedure is fully automatic with a specified confidence level for the statistics. Potential application to the heteroscedastic noise case is also demonstrated. Performance was assessed in simulations conducted on several synthetic spectra using traditional error measures as well as comparisons of local extrema in the resulting smoothed signals to those in the true spectra. For the simulated spectra, a best case comparison with the Savitzky–Golay smoothing via an exhaustive parameter search was performed while the SAPLS method was assessed for automated application. The application to several dissimilar experimentally obtained Raman spectra is also presented.