A comparison of Raman chemical images produced by univariate
and multivariate data processing—a simulation with an example
from pharmaceutical practice
Slobodan Šašić,*a,b Donald A. Clark,a John C. Mitchellb and Martin J. Snowdenb
a Pfizer Global Research and Development, Ramsgate Road, Sandwich, UK CT13 9NJ
b University of Greenwich, Medway Sciences, Chatham Maritime, UK ME4 4TB.
E-mail: [email protected]; Fax: 144 (0)1304 656726; Tel: 144 (0)1304 643250
Received 30th June 2004, Accepted 31st August 2004
First published as an Advance Article on the web 7th October 2004
A direct comparison of univariate and multivariate data analysis has been performed to show the effect of
spectral noise on the quality of chemical images derived from hyper-spectral data cubes. A data processing
approach has been developed using a numerical model, based on spectra of common pharmaceutical excipients,
and then applied to a real multi-layered solid dosage formulation. The results of this study demonstrate that
the multivariate analysis, which in its simplest form only de-noises data using principal component analysis
(PCA), produces significantly better quality chemical images than the univariate approach, even from data sets
which appear visually poor. If pure component spectra are available, ordinary least squares (OLS) regression
offers even better results. The ability to de-noise spectra using these approaches impacts on Raman
experimental conditions and increases information content collected per unit time. Data acquisition time, which
is a rate limiting step in the production of chemical images using Raman mapping and imaging techniques, is
reduced by 60% and still produces multivariate chemical images of appropriate quality with which to study
pharmaceutical formulations.
DOI: 10.1039/b409879j
Introduction
Raman mapping/imaging is a fast progressing application of
vibrational spectroscopy, although it was first described in
1975.1 It has been used in numerous applications that include
the pharmaceutical and polymer industries,2–6 in investigation
of biological/medical samples,7–12 archaeology,13 single molecule spectroscopy14,15 etc. An overview of instrumentation and
applications relating to this area can be found in ref. 16.
There are three kinds of laser light illumination (point and
line for the mapping systems and so-called wide field illumination for the imaging systems) that excite the sample in a Raman
mapping/imaging instrument.16 The instruments with the first
two sources provide high quality, full-range spectra allowing
different mathematical tools to be used in the process of
producing images. The wide field imaging equipment should
have much faster experiment times due to more specific
experimental conditions. However, these instruments do not
always provide spectra that are comparable in quality with
those from the instruments equipped with standard dispersion
optical elements. In addition, the main advantage of imaging
instruments (rapid production of images) holds only if the
scanning is carried out without collecting full spectra which
leads us to the question of how chemical images are in fact
formed.
The simplest and still most convenient approach to producing chemical images is the so-called univariate approach.
Here a chemical image is generated that represents the spatial
distribution of a component of interest based on its intensity at
a uniquely assignable Raman shift. The key requirement of
univariate imaging is a precise spectral characterization of the
sample before starting the imaging process, as the uniquely
assignable wavenumbers should be known in advance. Another
{ In this study ‘multivariate imaging’ refers to using the entire spectra
anywhere in the process of producing an image.
option is multivariate imaging{ that employs full spectra and is
tightly associated with chemometrics.17–21 There are several
examples (microdamage in a bone,17 separation of waste on
a conveyer belt,19 characterization of an emulsion21) that
illustrate how, via the multivariate approach, one can image
demanding samples for which there is very little background
information (which makes univariate approach practically
inapplicable).
The motivation behind the work reported herein is to
quantitatively compare performances of the univariate and
multivariate imaging techniques. To the best of our knowledge,
despite numerous publications, there are no studies that
compare these two methods side-by-side because the experimentalist generally selects the method that best fits the overall
conditions of the experiment. In addition, comparison of
chemical images can rarely be found in the scientific literature
because it is difficult to establish a reference or standard to
compare with an experimental image (except for the comparative study of Raman imaging instrumentation22). Therefore,
there is no literature data that numerically compare performances of the two approaches for producing images.
Furthermore, the technical aspects of different Raman
instruments need to be taken into consideration. The instruments that employ point and line sources produce spectra. The
information content is such that the multivariate approach will
always over-perform when compared to the univariate analysis
and should be used whenever possible. However, the univariate
approach fits well with wide-field illumination instruments and
that is why we consider it worth pursuing.
In this work we have produced and mapped a multicomponent model that contains components typically found in
a pharmaceutical tablet, and then considered a multi-layered
bead formulation as an example of a sample routinely analysed
in our laboratory. The results and conclusions of this study
compare the model and experimental data in terms of chemical
image quality and Raman spectral signal to noise ratio. The
This journal is ß The Royal Society of Chemistry 2004
Analyst, 2004, 129, 1001–1007
1001
study conclusions are discussed with respect to chemical
imaging in general.
Experimental
Creation of the spectral model
The spectra of five materials that are typically used in pharmaceutical products were used to build the spectral model.
These were micro-crystalline cellulose (hereafter called avicel),
explotab, di-calcium phosphate anhydrous (DCP), magnesium
stearate (MgSt) and active pharmaceutical ingredient (API).
The spatial distribution in the chemical images of these
components was created by assigning to them the following
contents: avicel 60%, DCP 31%, API 5%, explotab 3% and
MgSt 1%. The spatial distributions were created such that a
pixel in the image represents only one component. The model
simulates data collection over a 30 6 30 pixel area so that 1%
of MgSt means that 9 out of 900 pixels are assigned to this
excipient. Four pixels representing MgSt grouped together
represent the smallest cluster in all five chemical images. The
pixels which correspond to the spatial position of the components (y0 for absence and y1 for presence) are multiplied
with the pure component spectra. In this way, five 3D arrays or
hyper-spectral data cubes (30 6 30 spatial 6530 spectral
dimension) are obtained, one for each component. These pure
component data cubes are then co-added to create the noiseless
hyper-spectral model data cube. Different amounts of noise are
added to the model data cube. As Raman noise is dependent on
the intensity of the signal, multiplicative (heteroscedastic) noise
is generated and added to the pure data in the following way.
A normally distributed noise is created by a Matlab 6
(Mathworks, Natick, MA, USA) command, weighted by the
pure data, multiplied by the different constants, and then
added to the same data. This resulted in the presence of 1, 10,
25 and 35% of relative standard deviation (rsd) of noise for
each peak in the five corresponding data cubes, respectively.
The rsd is calculated from the series of spectra as the ratio
between the standard deviation and the mean at a peak
position. Fig. 1 shows an example of the spectra with 25% and
35% of noise. Note that the variations at the peaks are
exaggerated with respect to the spectra normally encountered
in practice, while the noise at the baseline appears negligible in
comparison with noise on the peaks. All the spectra are meannormalized (each spectrum is divided by its mean intensity).
Collection of the spectra
Raman images were collected on a Renishaw Ramascope
System 1000 using Wire V.1.3 software. The spectra were
obtained by exciting the sample with a laser line at 782 nm. The
sample was viewed and Raman data collected through a 620
objective. The data collection was set to cover the 200–
1800 cm21 range. Usually (and if possible) one selects the
spectral interval that does not involve movements of the
grating. For this instrument this covers a range of ca. 500 cm21.
However, in this case it was necessary to collect over the whole
fingerprint region in order not to miss potential univariate
points and this meant much longer data collection time due to
the grating scanning. The spectral resolution was reduced after
binning from the original y1 cm21 to y3 cm21. The spatial
resolution in the X dimension was 20 mm, set by the experiment
stepsize while in the Y dimension (along the excitation line) the
spatial resolution was determined by the relative CCD pixel
size. The spectra were not spatially binned prior to the analysis.
Sample preparation
The beads were halved with a scalpel to produce a flat surface
for chemical mapping. Only one half of the bead was mapped.
For the purpose of this work it was only important to recognize
the beads’ layers and collect the spectra from them. The composition of the bead is not discussed.
Data analysis
The chemical images of the model and the bead were created
from the data cubes in three ways: (1) by following the intensities at the wavenumbers which are specific for each component (univariate approach), (2) by de-noising the data via
principal component analysis (PCA)23,24 and then using the
same univariate analysis or (3) by using the pure component
spectra via ordinary least square (OLS) regression24 (this
option was not applied to the bead data because the pure
component spectra of the bead were not available).
The images from the model with varying noise were
binarized and compared with the binarized true images of
the species. Only pixels with the intensities above half of the
maximum intensity in an image of a component are displayed
in the binarized images. As mapping of the bead was a real
experiment, no true data were available for the bead images so
that the binarized univariate images of the bead’s components
were compared with the ones pre-processed by PCA.
Results
Model images
Fig. 1 A noiseless spectrum from the model and the two corresponding spectra with the relative standard deviations of noise of 25 and 35%
respectively (same noise, different amplitude).
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Analyst, 2004, 129, 1001–1007
The wavenumbers for each component that are used for
univariate imaging are shown in Fig. 2. The univariate point
associated with avicel is weakly selective as it is not at a peak
position and has a very weak intensity. Comparison between
the true images of the components and those obtained in a
univariate fashion is shown in Table 1. The term ‘difference’ in
Table 1 stands for the sum of absolute values obtained via
subtraction of the binarized images of the model components
from the corresponding true ones.
Evidently, 1% of noise does not represent a problem as the
binarized images of the model closely match the true ones. For
10% of noise in the model data a mismatch of 5–10% in the
position of white pixels (‘1’ in a binarized image) is detected.
For 25% of noise, however, the discrepancy is evident and
ranges between 20 and 40% in the positions of the white pixels.
Fig. 3 reveals that the image of avicel barely matches the true
one. Combining images of the components in order to make a
composite image of the investigated sample is not possible
with 25% of noise. This is because the here defined pixel
Fig. 2 The arrows mark the univariate points for the components of the model; (–) explotab, (– –) API, (–#–) MgSt, (?–?) avicel and (–.–) DCP.
Table 1
Avicel
API
MgSt
Explotab
DCP
a
Difference in the number of white pixels (see the text for explanation) in binarized images of the model as compared with the true data
Rsd of noise
1%
10%
25%
25%
35%
True
Method
Univariate
6 (1%)
0
0
0
5 (2%)
Univariate
25 (5%)
2 (6%)
0
1 (4%)
35 (12%)
Univariate
212 (39%)
13 (36%)
3 (33%)
4 (17%)
118 (40%)
Multivariate
50 (9%)
0
0
0
14 (5%)
Multivariate
35 (6%)
3 (8%)
0
1 (4%)
26 (8%)
548
36
9
23
294
‘Multivariate’ refers to noise elimination by PCA and subsequent imaging via univariate points.
thresholding criterion is vulnerable to considerable noise and
may lead to poor and unreliable composite images.
25% noise is not an issue for the multivariate approach even
for avicel the spectrum of which is highly overlapped. The
simplest form of this approach is to use a routine such as PCA
to de-noise the data and then to produce images via the
univariate points. The results obtained in this way can only be
better if additional multivariate tools are employed. The
eigenvalue analysis straightforwardly recognizes 5 components,
and after truncating the data so that only signal is retained, a
significant improvement in the quality of images is accomplished (Fig. 3). The discrepancies are now detected only for
the two most abundant species (Table 1).
Good results in multivariate imaging in the same way as
described above are obtained with 35% of noise, and with the
use of pure component spectra (OLS regression) even with 50%
of noise. However, the model with so much noise does not
convincingly correlate with reality so that these results are not
further commented on here.
Finally, an average error per all the pixels can be calculated
for each component. Using OLS regression on the spectral
model, the true data are quantitatively reconstructed, while for
univariate and PCA-univariate approaches the images had to
be re-scaled in order to match the original [0,1] interval. For
25% of noise, which is considered critical here, the average
error for the univariate approach varies from 22% for DCP to
32% for MgSt. For the multivariate approaches the errors are
much smaller and vary between 5 and 11% for the PCA
approach, and between 4 and 9% for the OLS regression. These
numbers refer to the grey scale images and as such they do not
fully take into account the spatial distributions but are very
useful in terms of quantification. An immediate outcome of this
comparison is that semi-quantitative imaging is possible via the
spectra with substantial noise, provided the hyper-spectral data
cube is collected and particularly if the pure component spectra
are available.
Bead images
The Raman image of the bead displayed in Fig. 4 reveals that
there are at least four potential layers to analyse. For the
purpose of this work, we concentrate only on the major components. Our first task is to relate noise employed in the model
with noise in the bead spectra. Fig. 5 shows the series of spectra
extracted from different points in the three visible layers with
highlighted noise on the peaks. Clearly, for the spectra in all
three layers the rsd of noise is inside the boundaries
investigated in the model so that the results from imaging
the model are expected to reasonably relate with imaging the
bead via both univariate and multivariate ways.
The univariate points for the layers of the bead are shown in
Fig. 6. The outer layer cannot be reliably imaged as the baseline
at its univariate point at 360 cm21 is poorly defined. The peak
at 1520 cm21 that is uniquely assignable to this layer cannot be
employed as the univariate point because the baseline variation
in that part of the spectra significantly interferes with the band
itself. On the other hand, the inner layer and the core have
much better prospects for univariate imaging due to a much
better definition of the univariate points (Fig. 6). According to
the model, these two layers may be successfully imaged because
the rsd at their univariate points is about 10%. If this assumption holds, the difference between the univariate and multivariate images (de-noising by PCA and imaging via the same
univariate points) should be small.
After binarizing the images of the three layers, the discrepancy of 4.4% in the number and position of the white pixels
in the multivariate and univariate images is found for the inner
layer, 11% for the core and 25% for the outer layer. The
difference in imaging the core is visualized in Fig. 7. This comparison reveals satisfactory agreement between the univariate
model and bead images for the given level of noise. For images
obtained by the multivariate approach, the de-noised Raman
spectra produce chemical images of high quality because PCA
effectively removes noise from the spectra. This is also in
Analyst, 2004, 129, 1001–1007
1003
Fig. 4 Raman image of the bead at 857 cm21. The size of the image is
approximately 1 mm 6 0.5 mm. The symbols mark the analysed layers.
Fig. 8 shows the spectra of the layers (compare with Fig. 5).
The decrease in the signal-to-noise ratio is substantial and
surprising as reducing the measurement time was not expected
to increase the rsd’s from Fig. 5 for more than 50%.25 In reality
the rsd was found to be between three and four times larger
than the values in Fig. 5. Fig. 8 suggests that an image of the
outer layer cannot be obtained by any approach, the inner layer
still has recognizable features, while many bands of the core are
buried in noise. The univariate and multivariate chemical
images of the three major layers of bead are displayed in Fig. 9.
While only the univariate chemical image of the inner layer
may be considered acceptable, the multivariate images of all
three layers are acceptable. The binarized univariate image of
the inner layer reasonably compares with the multivariate one
as the calculated spatial difference is 11%. The difference for
the core is 33% while it is pointless to compare images of
the outer layer because its univariate image is of intolerable
quality.
Discussion
Fig. 3 The true (A), univariate (B) and multivariate (C) grey images of
avicel.
agreement with the model that predicts superior performance of
the multivariate approach for an rsd of 10%. The obtained results
indicate that a reduction of the measurement time, i.e. increase of
noise, may still provide satisfactory multivariate images and
acceptable univariate images of the inner layer. To test this
hypothesis, the measurement time was reduced from 60 to 20 s
and the experiment repeated, albeit on another bead sample.
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Analyst, 2004, 129, 1001–1007
Owing to the amount of data collected and computations
involved, the multivariate approach produces reliable chemical
images and allows for full data exploration in both spectral and
spatial dimensions. The univariate approach hinges on the
premise of a precise definition of the investigated systems. If
something unexpected is encountered during the experiment
(e.g. the sample changes), or if the instrument premises are not
ideal (e.g. many cosmic events, temperature/humidity changes),
one may be unable to recognize and resolve the problem. Thus,
it is undisputable that the multivariate analysis is the favoured
data processing method, not only in chemical imaging but in
analytical spectroscopy in general. However, there are technical
issues accompanying collection of such a vast number of
spectra (usually measured in thousands when mapping or
imaging samples). Such Raman experiments are normally
performed on line or point mapping systems and may take
several days to collect the data. The current state of chemical
imaging hardware partially promotes global imaging systems,
as they rapidly image employing univariate imaging methodology. While the measurement time is not necessarily a key issue
for the pharmaceutical samples analysed here, it may be
crucially important whenever biological samples are imaged as
these may change with time or environmental conditions.
Therefore, there is a need to estimate the relation of univariate
versus multivariate data processing in terms of quality of
produced chemical images. The results presented in this work
quantitatively compare the performance of multivariate and
univariate data analysis for samples that are well defined, and
are equally applicable to any sample irrespective of its nature.
The criteria for estimating the noise within spectra and
quality of images employed in this work may appear simple
but are recognized in the literature,25 and are universally
Fig. 6 Univariate points (ƒ) for the outer (red) and inner layer (–),
and for the core (– –).
Fig. 7 Cropped and binarized univariate (A) and multivariate
(B) images of the core in Fig. 4.
Fig. 5 The series of spectra obtained from different positions on the
bead: the outer layer (A), the core (B) and the inner layer (C). The
numbers denote rsd (in %) at the peak positions.
understandable and applicable. One has to be aware, however,
that the definition of the threshold for binarizing images is a
very sensitive issue specifically if intimately mixed samples are
imaged. The criterion selected here seems functional when
spatially well resolved solid samples are investigated but it
should not be generalized as it may ignore minor components
of sub-pixel size mixed samples, or in the images with poor
spatial resolution. In such cases there is a significant risk of
obtaining overlapped images of the single components. In
order to avoid that, a more thorough criterion for pixel
thresholding must be proposed.
Table 1 and Figs. 5, 7, 8 and 9 illustrate the empirical target
values for signal-to-noise ratio in the Raman spectra with
respect to producing chemical images. The simulation suggests
that even 10% of noise, as defined here, produces relatively
small differences between the univariate and multivariate
images. When tested on the real sample this prediction proves
rather accurate. Furthermore, as one intuitively expects, the
only criterion for successfully imaging a component is the
strength of a component’s signal provided that there is no
interference from neighbouring pixels. The simulation shows
that whilst MgSt is present at a low concentration, it is in fact
easy to image because of its strong spectral response in the
model data. The 60 times more abundant avicel represents a
demanding target due to its weakly effective univariate point.
In terms of the multivariate approach, both model and bead
chemical images are encouraging as they are produced using
visually unacceptable spectra (Figs. 1 and 8). The ability of
PCA to eliminate noise is impressive though we assume that
this may be a consequence of the high compactness of the data
explored here.
As mentioned above, we briefly touched on the performance
of OLS regression. It is clear that, provided there is a good
match between the pure component and experimental spectra,
OLS images can only be of higher quality than those obtained
via PCA because they have higher information content. OLS
regression is not often used in analytical spectroscopy as it is
rarely possible to confidently recognize all the components that
contribute to the experimental spectra. However, there are at
least two groups that intensively practise OLS regression in
analysing vibrational spectra of biological samples.26–29 The
results of this work suggest that if a biological sample under
investigation is spectroscopically precisely defined, meaning
OLS is applicable as a data processing tool, then there is a good
prospect of fast data acquisition from such a sample. If single
vibrational spectra are measured, precise concentrations or
Analyst, 2004, 129, 1001–1007
1005
classification lines from the spectra of relatively poor quality
may be determined via OLS. For the sample analysed here, it is
relatively easy to provide the spectra of the components that
form the bead, so that the prospects of fast data acquisition and
imaging the beads (or samples of comparable structure) are
much better. In addition, if anything unexpected takes place
during the experiment, it may be trivial to ascertain the
chemical nature of the change (e.g. by analysing residuals
between the original and via OLS reconstructed data).
Our attempt to significantly reduce the collection time
without a comprehensive loss of image quality was successful
for the multivariate analysis whilst the performance of the
univariate approach was somewhat below the expectation. The
60 s data measurement provides acceptable images by
univariate analysis for two investigated components while for
the third one only a much longer collection time may lead to
better images (Figs. 5 and 7). After reducing the collection to
20 s, only one layer is successfully imaged by the univariate
approach (Fig. 9, middle). The estimated increase in rsd with
reduction of measurement time was based on the dt
dependence of signal-to-noise ratio in Raman spectroscopy.25
However, as the spectra used for calculating rsd were selected
from various points on the bead, other factors may adversely
contribute to the rsd making dt dependence too optimistic.
Still, the spectra in Fig. 8 are far too noisy. The unexpectedly
higher noise level may be attributed to a higher level of
fluorescence (the fluorescence background is eliminated from
all the spectra shown here). In addition, the baseline interference is notable. One may argue that a weakness of the model
is that it ignores baseline noise as most of the peaks in the
model are clearly above the baseline. What this study has not
addressed is the situation when the Raman signal is comparable
to the background noise. Another study, that carefully
monitors and explores baseline variations, is required for this
case. Nonetheless, the data from the model are clearly helpful
for comparing the quality of univariate and multivariate data
processing approaches, and for empirically relating the quality
of obtained chemical images with the criterion for signal-tonoise ratio in the hyper-spectral data cubes.
Conclusion
Fig. 8 The same as in Fig. 5 with the data collection time being only
one third of that used for the spectra in Fig. 5.
Fig. 9 The univariate (top) and multivariate (below) images of the
layers of the bead mapped for 20 s.
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Analyst, 2004, 129, 1001–1007
This study reports on the influence of 1, 10, 25 and 35% of noise
(ratio of rsd at the peak maximum to the mean maximum in a
set of spectra) on the quality of images obtained from the
artificial hyper-spectral data cubes. The images are obtained in
univariate and multivariate ways, the latter referring to PCA
used only for noise elimination, or to OLS regression. The
comparison of the binarized true and model images shows that
the univariate approach is reasonably effective between 1 and
10% of rsd at the peaks but fails at 25% of rsd. On the other
hand, the multivariate approach in its simplest form efficiently
reduces noise and produces high quality chemical images
despite the presence of substantial, even exaggerated noise in
the original data. The results of the OLS regression seem even
more optimistic. The model spectra are related to the Raman
spectra obtained by mapping pharmaceutical samples. It is
found that the spectra collected during routine mapping of a
bead are inside the boundaries of noise used in the model so
that the conclusions from the model can be verified on the bead
images. The differences between the chemical images of the
layers of the bead created by the univariate and multivariate
approaches are more pronounced than expected. Using the
results from the model, a mapping experiment is conducted
with dramatically reduced measurement time. As the noise has
increased above the prediction, the univariate approach
becomes practically inapplicable. However, the multivariate
approach still produces high quality images despite the Raman
spectra being visually of a very low quality.
Acknowledgements
We thank Drs R. Brody and A. de Paepe of Pfizer Global
Research and Development for useful discussions.
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