prospectr (version 0.2.7)

detrend: Detrending spectral data

Description

Normalizes each row of an input matrix by applying a SNV transformation followed by fitting a second order linear model and returning the fitted residuals.

Usage

detrend(X, wav, p = 2)

Value

a matrix or vector with the detrended data.

Arguments

X

a numeric matrix or vector to process (optionally a data frame that can be coerced to a numerical matrix)

wav

the wavelengths/ band centers.

p

an integer larger than 1 indicating the polynomial order (default is 2, as in the original paper of Barnes et al., 1989).

Author

Antoine Stevens and Leonardo Ramirez-Lopez

Details

The detrend is a row-wise transformation that allows to correct for wavelength-dependent scattering effects (variations in curvilinearity). A pp order polynomial is fit for each spectrum (x_ix_i) using the vector of bands (, e.g. wavelengths) as explanatory variable as follows:

x_i = a^p + ... + b + c + e_ix_i = a^p + ... + b + c + e_i

were a, b, c are estimated by least squares, and e_ie_i are the spectral residuals of the least square fit. The residuals of the iith correspond to the iith detrended spectrum.

References

Barnes RJ, Dhanoa MS, Lister SJ. 1989. Standard normal variate transformation and de-trending of near-infrared diffuse reflectance spectra. Applied spectroscopy, 43(5): 772-777.

See Also

standardNormalVariate, blockScale, blockNorm

Examples

data(NIRsoil)
wav <- as.numeric(colnames(NIRsoil$spc))
# conversion to reflectance
opar <- par(no.readonly = TRUE)
par(mfrow = c(2, 1), mar = c(4, 4, 2, 2))
# plot of the 10 first spectra
matplot(wav, t(NIRsoil$spc[1:10, ]),
  type = "l",
  xlab = "",
  ylab = "Absorbance"
)
mtext("Raw spectra")
det <- detrend(NIRsoil$spc, wav)
matplot(wav, t(det[1:10, ]),
  type = "l",
  xlab = "Wavelength /nm",
  ylab = "Absorbance"
)
mtext("Detrend spectra")
par(opar)