Digital Restoration of Separations Data

Abstract

In experimental separations, the acquired signal can have four common but unwanted elements: (i) high-frequency noise, (ii) drift, (iii) occasional periodic and pink noise, and (iv) a mixture of components traveling with close velocities. Additionally, separation scientists observe partially resolved peaks in chromatographic or capillary electrophoresis detector output. A protocol for digitally recovering the “true data” is provided with clear-cut details and open-access codes for formulating denoising, baseline correction, and peak resolution problems as linear or nonlinear optimizations. The smoother of Bohlmann–Whittaker denoises and preserves the total area of the signal. Fourier transform methods to detect and remove periodic noise are also proposed for erratic periodic noise problems. A peak width preserving filter, called the bilateral filter, is also given. This procedure is followed by two reliable baseline correction algorithms based on asymmetric reweighted least squares or curvature-based weights to deal with low-frequency signal variations. Once low- and high-frequency noise components are removed, a convenient peak mode location method is introduced, relying upon numerically stable second derivative calculation from Savitzky–Golay (SG) filter. Peak locations, area, height, and higher statistical moments can be derived from iterative curve fitting. The protocol shows two peak models that can model left or right skewed peaks. The new peak models are (i) a numerically stable version of the bi-directional exponentially modified Gaussian (EMG), suitable for a wide variety of real chromatograms, and (ii) the twice generalized normal model with third- and fourth-moment parameters built into it. The nonlinear least squares regression approach uses the trust-region reflective optimization method. The algorithm converges to a solution even with multiple peaks and approximate guesses of peak parameters. The protocol can be generalized to fit more than 200 peak functions in separation sciences available in literature by minor adaptations of the provided codes in the MATLAB environment.