detrend {prospectr}

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)

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).

Details

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

\[x_i = a\lambda^p + ... + b\lambda + c + e_i\]

were a, b, c are estimated by least squares, and \(e_i\) are the spectral residuals of the least square fit. The residuals of the \(i\)th correspond to the \(i\)th detrended spectrum.

Value

a matrix or vector with the detrended data.

Author(s)

Antoine Stevens and Leonardo Ramirez-Lopez

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)