The multiplicative scatter correction has been proposed as method in
NIR spectroscopy to correct signals for noise. Light scattering or change
in path length for each sample is estimated relative to that of an ideal
sample. In principle this estimation should be done on a part of the spectrum
which does not contain chemical information, i.e. influenced only by the
light scattering. However the regions in the spectrum that hold no chemical
information often contain the spectral background where the signal to
noise ratio may be poor. In practice the whole spectrum is sometimes used.
This can be done provided that chemical differences between the samples
are small. Each spectrum is then corrected so that all samples appear
to have the same scatter level as the ideal.
As an estimate of the ideal sample, we can use for instance the average
of the calibration set. Multiplicative scatter correction performs best
if an offset correction is carried out first. For each sample:
xi: the ith spectrum of the collection used
b: For each sample, a
and b are estimated by ordinary
least-squares regression of spectrum xi versus yAverage
over the available wavelengths j.
Each value xij of the corrected
(MSC) is calculated as:
xij: the intensity
of the ith spectrum and jth wavelength of the collection
used for calculation.