Improved Piecewise Orthogonal Signal Correction Algorithm

Abstract

Piecewise orthogonal signal correction (POSC), an algorithm that performs local orthogonal filtering, was recently developed to process spectral signals. POSC was shown to improve partial leastsquares regression models over models built with conventional OSC. However, rank deficiencies within the POSC algorithm lead to artifacts in the filtered spectra when removing two or more POSC components. Thus, an updated OSC algorithm for use with the piecewise procedure is reported. It will be demonstrated how the mathematics of this updated OSC algorithm were derived from the previous version and why some OSC versions may not be as appropriate to use with the piecewise modeling procedure as the algorithm reported here.

Wavelet orthogonal signal correction

“…Specifically, the corn data were chosen to show, through a comparative study of the moisture example, that WOSC preprocessing addresses a possible limitation of piecewise OSC [16,17]: it permits correction of broad analyte signals that are not localized in the time domain.…”

“…Also depicted in Figure 3 is the external prediction curve of moisture content for piecewise OSC [16,17]. POSC is a local filter in which a separate OSC step is conducted within a narrow spectral region of the data.…”

“…However, forcing the filtered variance in X to be exactly orthogonal to the property information tends to overfit the data, since it disregards the effect of measurement error in y [22]. In addition, the use of a tight orthogonality restriction generally does not allow for the sufficient removal of background, since these effects are, in many cases, not precisely orthogonal to the property vector [17]. For these reasons the OSC methods that do not impose a strict constraint are usually preferred for signal preprocessing, even though there is potential for loss of some chemical information.…”

“…To truly benefit from OSC preprocessing, the variance described with OSC should be localized prior to PLS regression [16,17]. This localization can be accomplished by combining OSC and wavelets in a multiscale fashion.…”

“…It is demonstrated with two NIR data sets that more robust PLS calibrations with improved predictive ability can be constructed from data pretreated with WOSC than from data pretreated with either OSC or the wavelet prism independently. Similarly, it is shown that the approach taken in WOSC may also be beneficial to piecewise OSC (POSC) [16,17], another local OSC filter, for the correction of signals with broad analyte bands.…”