443
15 FtIR Imaging of tissues: techniques and methods of Analysis
where T represents the score matrix and P the loadings matrix. the first few loadings describe the majority of the variance. these loadings are incorporated into the
EmSC model in the following manner.:
Z
Z
p E
raw
r ef
i i
a m
b
g
= + ( ) +
+
+
∑
ν
1
7
(15.14)
where the g i are the weights applied to the loading vector p i . this expression can be
re-arranged to give the corrected spectrum.:
Z
Z
p
corr
raw
i i
a m
g
b
=
−
+
+
∑
ν
1
7
(15.15)
15.4.5 Other Methods to Correct for Dispersion and Mie
Scattering
the diem group introduced a phase correction approach that is based on the notion
that the complex Fourier transform can be separated into the real and imaginary
parts of the spectrum or interferogram by varying the phase angle between them.
using the mertz algorithm, a wavenumber-dependent phase angle can be calculated
and phase corrected spectra computed by a complex forward Fourier transformation
of the real and imaginary part of the spectrum or interferogram [82]. the advantage
of this approach is the computation time is dramatically reduced.
15.4.6 Unsupervised Hierarchical Cluster Analysis
there are three main ways to present FtIR spectral data, namely univariate (chemimages), multivariate and pattern recognition. univariate methods are typically
based on determining the absolute intensity of a band, or the ratio of two bands or
are based on determining the integrated area of a band between two baseline points.
these maps provide quantitative information on macromolecules in a cell or tissue
sample but are generally not diagnostically useful. multivariate methods make use
of spectral similarity to generate false-colour maps. there are many approaches to
generate multivariate images from spectral data hypercubes. these include unsupervised hierarchical Cluster Analysis (uhCA), K-nearest neighbours (K-means),
Principal Component Analysis (PCA) and artificial neural networks (ANNs) to
name a few. unsupervised hierarchical Cluster Analysis (uhCA) is a proven technique for image reconstruction with FtIR data [83–85]. In cluster analysis, a matrix
is calculated that expresses the similarity, or ‘‘distance’’, between each spectrum
15 FtIR Imaging of tissues: techniques and methods of Analysis
where T represents the score matrix and P the loadings matrix. the first few loadings describe the majority of the variance. these loadings are incorporated into the
EmSC model in the following manner.:
Z
Z
p E
raw
r ef
i i
a m
b
g
= + ( ) +
+
+
∑
ν
1
7
(15.14)
where the g i are the weights applied to the loading vector p i . this expression can be
re-arranged to give the corrected spectrum.:
Z
Z
p
corr
raw
i i
a m
g
b
=
−
+
+
∑
ν
1
7
(15.15)
15.4.5 Other Methods to Correct for Dispersion and Mie
Scattering
the diem group introduced a phase correction approach that is based on the notion
that the complex Fourier transform can be separated into the real and imaginary
parts of the spectrum or interferogram by varying the phase angle between them.
using the mertz algorithm, a wavenumber-dependent phase angle can be calculated
and phase corrected spectra computed by a complex forward Fourier transformation
of the real and imaginary part of the spectrum or interferogram [82]. the advantage
of this approach is the computation time is dramatically reduced.
15.4.6 Unsupervised Hierarchical Cluster Analysis
there are three main ways to present FtIR spectral data, namely univariate (chemimages), multivariate and pattern recognition. univariate methods are typically
based on determining the absolute intensity of a band, or the ratio of two bands or
are based on determining the integrated area of a band between two baseline points.
these maps provide quantitative information on macromolecules in a cell or tissue
sample but are generally not diagnostically useful. multivariate methods make use
of spectral similarity to generate false-colour maps. there are many approaches to
generate multivariate images from spectral data hypercubes. these include unsupervised hierarchical Cluster Analysis (uhCA), K-nearest neighbours (K-means),
Principal Component Analysis (PCA) and artificial neural networks (ANNs) to
name a few. unsupervised hierarchical Cluster Analysis (uhCA) is a proven technique for image reconstruction with FtIR data [83–85]. In cluster analysis, a matrix
is calculated that expresses the similarity, or ‘‘distance’’, between each spectrum