Principal component analysis (PCA) and principal component regression (PCR)
are widespread algorithms for calibration of spectrometers and evaluation
of unknown measurement spectra. In many measurement tasks, the amount of ca
libration data is increasing nowadays due to new devices like hyperspectral
imagers. Core of PCA is the singular value decomposition (SVD) of the matr
ix containing the calibration spectra. SVD of large calibration sets is com
putational, very expensive and often gets unreasonable due to excessive cal
culation times.
With hyperspectral imaging as application in mind, an algorithm is proposed
for compressing calibration spectra based on a wavelet transformation befo
re performing the SVD. Considering only relevant wavelet coefficients can a
ccelerate the SVD. After determining the relevant principal components (PCs
) from this shrunken calibration matrix in the wavelet domain, they are exp
anded again by insertion of zeros at the right positions. Denoised PCs are
then obtained by the inverse wavelet transform into the wavelength domain.
An additional computation speed increase is described for "landscape" matri
ces by transposing the matrix before performing the SVD. In the Results sec
tion, both PCA approaches are demonstrated to result in comparable PCs. Thi
s is done by means of synthetically generated spectra as well as by experim
ental FTIR-data. By this algorithm, the PCA of the discussed examples could
be accelerated up to a factor of 52. Additionally, concentrations of synth
etic spectra are evaluated by means of the PCs obtained by the different PC
A algorithms. Both PC sets, the conventional and the one based on the new t
echnique, result in equivalent concentration values. (C) 2001 Elsevier Scie
nce B.V. All rights reserved.