COMPARATIVE STUDY OF BLIND SOURCE SEPARATION

METHODS FOR RAMAN SPECTRA

Application on Numerical Dewaxing of Cutaneous Biopsies

Valeriu Vrabie

†

, Cyril Gobinet

‡

, Michel Herbin

†

and Michel Manfait

‡

†

CReSTIC, Universit´e de Reims Champagne-Ardenne, Chauss´ee du Port, 51000 Chˆalons-en-Champagne, France

‡

M´eDIAN, CNRS UMR 6142, Universit´e de Reims Champagne-Ardenne, 51 rue Cognacq Jay, 51096 Reims, France

Keywords:

Raman Spectroscopy, Parafﬁn-Embedded Cutaneous Biopsies, Blind Source Separation, Independent Com-

ponent Analysis, Non-negative Matrix Factorization, Maximum Likelihood Positive Source Separation.

Abstract:

Raman spectroscopy is a powerful tool for the study of molecular composition of biological samples. Digital

processing techniques are needed to separate the wealthy but complex information recorded by Raman spec-

tra. Blind source separation methods can be used to efﬁciently extract the spectra of chemical constituents.

We propose in this study to analyze the performances of four blind source separation methods. Two Inde-

pendent Component Analysis methods using the JADE and FastICA algorithms are based uniquely on the

independence of the spectra. The Non-Negative Matrix Factorization takes into account only the positivity of

underlying spectra and mixing coefﬁcients. The Maximum Likelihood Positive Source Separation assumes

both the independence and positivity of the spectra. A realistic simulated dataset allows a quantitative study of

these methods while a real dataset recorded on a parafﬁn-embedded skin biopsy provides a qualitative study.

1 INTRODUCTION

Raman spectroscopy is a light scattering technique

used in numerous biomedical applications (Choo-

Smith et al., 2002). For example, it was success-

fully used in oncology to discriminate between ma-

lignant and benign tumors (Haka et al., 2002; Gni-

adecka et al., 2004). Recording the Raman scattering

of a laser on a biopsy, the Raman spectroscopy gives

information about the vibrational modes of the ana-

lyzed sample. Based on the uniqueness of Raman sig-

natures of each molecular constituent, this technique

extracts wealthy but complex information about the

molecular composition of biopsies.

To be studied in optimal and reproducible condi-

tions by Raman spectroscopy, thin sections of biop-

sies are required. A conservative property of these

biopsies is also needed for their storage in tissue

banks (tumor banks in oncology) for further analysis.

To satisfy these requirements, the biopsies are ﬁxed

by formalin and embedded into parafﬁn. However,

the parafﬁn has a Raman signature made up of ener-

getic peaks that strongly overlap the signature of the

biopsy. Visual analysis of Raman bands (shape, wave-

length localization, etc.) or classical signal process-

ing methods such as Principal Component Analysis

(Haka et al., 2002) will be biased for a signature ex-

traction objective. A solution is to chemically dewax

and rehydrate the biopsies before analyzing them by

Raman spectroscopy. Nevertheless, this process has

several drawbacks such as: it is time and reagent con-

suming, the biopsies are altered and a residual layer

of parafﬁn may remain (Faol´ain et al., 2005).

To overcome these problems, an advanced signal pro-

cessing method based on Independent Component

Analysis (ICA) was recently proposed (Vrabie et al.,

2007). This method has been shown efﬁcient to model

the recorded spectra as a linear mixing of independent

Raman spectra, allowing to extract the signatures of

the parafﬁn and, thus, to numerically dewax the biop-

sies. It also allows to extract the spectrum of the un-

derlying biopsy (human skin) and therefore to deﬁne

molecular descriptors speciﬁc to melanomas and nevi.

However, the extraction of Raman spectra is not per-

fect because some residual parafﬁn peaks remain on

estimated spectra. This might be a consequence of es-

timated negative peaks, as this method does not take

into account the positivity of the spectra and associ-

349

Vrabie V., Gobinet C., Herbin M. and Manfait M. (2008).

COMPARATIVE STUDY OF BLIND SOURCE SEPARATION METHODS FOR RAMAN SPECTRA - Application on Numerical Dewaxing of Cutaneous

Biopsies.

In Proceedings of the First International Conference on Bio-inspired Systems and Signal Processing, pages 349-354

DOI: 10.5220/0001064903490354

 SciTePress

ated mixing coefﬁcients.

In this paper we propose a comparative study of

four methods of blind source separation for numerical

dewaxing of parafﬁn-embedded skin biopsies. The

ﬁrst one employs the Joint Approximate Diagonaliza-

tion of Eigenmatrices (JADE) algorithm (Cardoso and

Souloumiac, 1993). The second one, named FastICA

(Hyv¨arinen et al., 2001), uses a fast ﬁxed-point algo-

rithm. It is employed here in its deﬂation scheme in

which the spectra are estimated one by one. These

two methods are ICA-based methods that only as-

sume the independence of the spectra to be estimated.

Next, we consider the Non-Negative Matrix Factor-

ization (NMF) which takes into account only the pos-

itivity of underlying spectra and mixing coefﬁcients

(Lee and Seung, 1999). Finally, the Maximum Like-

lihood Positive Source Separation (MLPSS) assumes

both the independence and positivity of the spectra to

be estimated and was developed for the blind separa-

tion of Raman spectra (Moussaoui, 2005). A quantita-

tive study is proposed by considering the results given

by these methods on a realistic simulated dataset,

while a qualitative study is illustrated on a dataset

recorded on a parafﬁn-embedded skin biopsy.

2 RAMAN SPECTRA

The Raman spectrum R

is deﬁned as a N

di-

mensional vector made up by the Raman intensities

recorded at different wavenumbers into a measure-

ment point k. By scanning K points of a sample,

the Raman spectroscopy provides a matrix dataset

R = [... , R

, ...] ∈ R

K×N

The recorded dataset R can be modeled as a lin-

ear sum of spectra S

∈ R

of chemical constituents,

called also sources, weighted by the corresponding

mixing coefﬁcients A

∈ R

, called also concentra-

tion proﬁles (Vrabie et al., 2007):

R =

∑

i=1

+ N

. (1)

The noise N

describes a part of the noise that is made

up by sources related to useless chemical constituents

that might be present in acquisition or by a linear ad-

ditive recorded noise. The noise N

denotes a non-

linear additive noise (i.e. not having a linear behavior

from a spectrum to another) made up principally by

slow-varying parasitic ﬂuorescence. Since they are

generated by unrelated phenomena, the noise N

supposed decorrelated from the interesting spectra S

Note that the spectra of the chemical constituents and

the mixing coefﬁcients admit only positive values by

deﬁnition.

This model does not take into account the deform-

ing effects that might appear in real acquisitions such

as the spectral shifts or width variations of the Raman

peaks. These deforming effects and the noise N

can

be removed from the recorded spectra by preprocess-

ing techniques (Gobinet et al., 2007). We note there-

after with R

sig

= R − N

the subspace of dimension

P obtained after the preprocessing, which is made up

by the interesting spectra and the linear noise N

For parafﬁn-embedded biopsies, the value of M

can be usually ﬁxed at 5 for cases where the Ra-

man signature of the ﬁxation slide (as for example

CaF

slide) is owing to the recorded spectral range

or at 4 otherwise. Moreover, it was proved that

the parafﬁn is completely described by three sources

having non-overlapping thin peaks (Vrabie

et al., 2007). These sources being modeled as sparse

and non-Gaussian, all higher-order cross cumulants of

the M sources considered in (1) vanish, assuring the

independence of these sources.

Retrieving the spectra of the chemical constituents

can be thus formulated as a source separation problem

based on the assumption that these sources are posi-

tive and independent.

3 BSS METHODS

Blind source separation (BSS) consists in recovering

unobserved sources S

from several observed mix-

tures R with no a priori information about the mix-

ing coefﬁcients A

. The lack of a priori knowledge

about the mixture is compensated by physically plau-

sible assumption on the sources such as decorrelation,

independence and/or positivity. A review of the BSS

approaches can be found in (Cardoso, 1998).

BSS methods usually suppose that the number of

sources is smaller than the number of observed mix-

tures and that the dataset is noise-free. Generally, the

number of recorded spectra (i.e. K in our case) be-

ing at least one hundred spectra, the ﬁrst assumption

holds. The second one is not respected by the sub-

space R

sig

since the noise N

remains after the pre-

processing. Based on the assumption that this noise

is decorrelated from the interesting spectra, it can be

estimated and removed by decomposing the subspace

sig

in two orthogonal subspaces by the use of the

Singular Value Decomposition (Vrabie et al., 2007):

sig

∑

j=1

∑

j=M+1

, (2)

Note that this decomposition can be linked with the

well known Principal Component Analysis (PCA).

The second subspace is an estimate of the noise

BIOSIGNALS 2008 - International Conference on Bio-inspired Systems and Signal Processing

350

. The ﬁrst subspace is constructed by decorrelated

spectra

, which are still a linear mixing of inter-

esting spectra, and ﬁt the BSS model. The spectra

of parafﬁn being modeled by independent sources,

stronger criteria than decorrelation must be used to

extract them. Note that this decomposition may intro-

duce negative values in the ﬁrst subspace, especially

when the recorded intensities are weak, which is not

usually the case in Raman spectroscopy. In these

cases, the above subspace reduction can be replaced

by a random projection of the dataset R

sig

into a pos-

itive matrix having M lines (Moussaoui, 2005).

3.1 ICA

The Independent Component Analysis (ICA) is a

computational technique for the BSS problem based

on the only assumption that the sources are mutu-

ally independent and at most one is Gaussian. A de-

tailed description can be found in (Hyv¨arinen et al.,

2001). We focus here only on two ICA algorithms:

JADE (Cardoso and Souloumiac, 1993) and FastICA

(Hyv¨arinen et al., 2001).

ICA has two indeterminacies: the energies (vari-

ances) and the order of the independent components

(estimated spectra) cannot be determined. The ﬁrst

ambiguity is avoided by estimating independent com-

ponents of unit variances. This is not a restriction

for this kind of application since we are interested to

identify the spectrum of the biopsy in order to ﬁnd

molecular descriptors. Moreover, the ambiguity of

the sign of the estimated spectra is not avoided, but

this is insigniﬁcant since the sign can be found in the

mixing coefﬁcients. For these reasons and to simplify

the theory and the algorithms, the dataset R

sig

is cen-

tered by subtracting the mean of each spectrum. Each

observation is also normalized to unit variance, ensur-

ing that even weak-amplitude recorded observations

are well represented within the input data.

3.1.1 JADE Algorithm

The 4

order cross-cumulants of the decorrelated

sources

given by PCA in Eq. (2) are ﬁrstly com-

puted. A M × M × M × M dimensional tensor is ob-

tained, which must be diagonalized in order to ﬁnd

independent sources. The Joint Approximate Diago-

nalization of Eigenmatrices (JADE) algorithm (Car-

doso and Souloumiac, 1993) uses the joint diagonal-

ization of cumulant matrices obtained by unfolding

the obtained 4

order tensor. This step provides a

M × M rotation matrix B that is used to ﬁnd indepen-

dent sources

by multiplying the matrix made up by

the decorrelated sources

with this matrix B. The

’s are centered and normalized estimators of the in-

teresting spectra S

3.1.2 FastICA

The FastICA algorithm is based on a ﬁxed-point iter-

ation scheme for ﬁnding directions in which the ne-

gentropy is maximized. Beyond the very fast conver-

gence of this algorithm (at least quadratic), the algo-

rithm ﬁnds directly independent components of (prac-

tically) any non-Gaussian distribution using a nonlin-

earity g, so no estimate of the probability distribution

function has to be ﬁrst available. The nonlinearity can

optimize the performance of the method allowing to

obtain algorithms that are robust and/or of minimum

variance. Moreover, the independent components can

be estimated one by one, which is equivalent to a pro-

jection pursuit. A detailed description of this algo-

rithm can be found in (Hyv¨arinen et al., 2001).

This algorithm was employed here in its deﬂa-

tion scheme. The algorithm iteratively ﬁnds direc-

tions in which the estimated independent components

are maximally nongaussian. This technique is appro-

priate to initially estimate the spectra of the parafﬁn

. The spectrum of the biopsy is hence ob-

tained by deﬂation as the remaining source.

3.2 NMF

Broadly speaking, the Non-Negative Matrix Factor-

ization (NMF) factorizes a matrix made up of non-

negative values in two other matrices composed of

non-negative values, which multiplied will approxi-

mately equalize the original result (Lee and Seung,

1999). The factorization algorithms are based on iter-

ative updates which minimize a criterion such as the

least squares error or generalized Kullback-Leibler di-

vergence. These algorithms can only be guaranteed to

ﬁnd local minima, rather than a global minimum, and

the obtained results depend on the initialization.

The NMF using a least squares error algorithm

was used here in order to test if it is possible to ﬁnd

positivespectra S

and mixing coefﬁcients A

from the

dataset R

sig

without further a priori information.

3.3 MLPSS

The Maximum Likelihood Positive Source Separation

(MLPSS) assumes both the independence and posi-

tivity of the spectra to be estimated and has been de-

veloped especially for the blind separation of Raman

spectra (Moussaoui, 2005). It models the positive in-

dependent spectra to be estimated by gamma prob-

ability density functions (pdf) with an α parameter

COMPARATIVE STUDY OF BLIND SOURCE SEPARATION METHODS FOR RAMAN SPECTRA - Application on

Numerical Dewaxing of Cutaneous Biopsies

351

greater than one. This model is well adapted to spec-

tra of the parafﬁn S

To solve this problem, two algorithms were pro-

posed. The ﬁrst one is based on the maximization of

the likelihood by using a Monte-Carlo Expectation-

Maximization scheme, while the second one com-

bines the above assumptions and the maximum like-

lihood technique to derive a steepest gradient algo-

rithm. This last algorithm was used here because it is

faster and it is well adapted for cases where the noise

is small, which is the case of large acquisitions after

the noise removal by PCA.

3.4 Application

A quantitative study on a realistic simulated dataset is

ﬁrstly presented followed by a qualitative study on a

dataset recorded on a parafﬁn-embedded skin biopsy.

3.4.1 Simulated Dataset

We consider here four spectra S

,...,S

∈ R

990

rep-

resented in Figure 1. The ﬁrst three were constructed

from a recording on a parafﬁn block. The peaks were

selected by the use of a Hanning window accordingly

with the fact that the parafﬁn is deﬁned by three spec-

tra (Vrabie et al., 2007). The last one is the spectrum

of the human skin estimated on a real dataset by an

ICA-based BSS method. Note however that linear in-

terpolations were used to eliminate the imperfections

corresponding to contributions of parafﬁn peaks.

Figure 1: Simulated spectra.

These spectra were linearly mixed to construct K =

250 observations by randomly picking positive mix-

ing coefﬁcients from a mixing matrix obtained on a

real dataset. Figure 2 shows one observation. The

mixing coefﬁcients of S

are very low compared to

the others, due to the energetic Raman signatures of

the parafﬁn that are present in real acquisitions. Note

that this dataset is free of noise, so the decomposition

given in Eq. (2) was not performed here.

Figure 2: Example of one observation.

The number of sources to be estimated was set at

M = 4 for all BSS methods. The dataset was centered

and each observation normalized to unit variance be-

fore applying the ICA-based methods. A ”pow3”

nonlinearity g was chosen for the FastICA because

it gives the best estimator for the last spectrum.

The threshold of the least squares error algorithm

for NMF was set at 10

−10

. As the convergence was

very slow, a second stop condition was used: the vari-

ations of the least squares error from one iteration to

other must be smaller than 10

−5

. Even in this case the

convergence was very slow, the number of iterations,

which depends on the initialization, was about 6· 10

Note that the results presented here are the best ob-

tained for 20 different initializations of the NMF.

The gradient step size of the MLPSS method was

set at 10

−3

, which is a usual valuefor this kind of data.

The MLPSS method has a faster convergence than

NMF, around 10

iterations are necessary to obtain

a good estimate of the spectra. However, the MLPSS

did not have a convergence toward a stationary point,

so it was stopped after 5· 10

iterations.

Figure 3 shows the estimated spectra

of the last

spectrum S

by the presented BSS methods. We fo-

cus here only on this spectrum because it corresponds

to the underlying biopsy in real applications and its

estimation is of interest.

Figure 3: Estimators of the 4

spectrum. From top to bot-

tom: JADE, FastICA, NMF and MLPSS.

As we can see, the NMF fails to estimate this spec-

trum. This is due to the fact that NMF requires the

existence of a monomial submatrix in the dataset in

order to ensure the convergence of the algorithm to

the right solution (Moussaoui, 2005). The MLPSS

BIOSIGNALS 2008 - International Conference on Bio-inspired Systems and Signal Processing

352

provides a good positive estimate with few imperfec-

tions corresponding to contributions of parafﬁn peaks

at 1065 cm

−1

and 1300 cm

−1

. The two ICA-based

methods give the same results. The estimated spec-

tra have zero mean and unit variance and follow the

shape of the original spectrum except some imper-

fections at 1175 cm

−1

and 1470 cm

−1

. Note that all

estimated mixing coefﬁcients have uniquely positive

values, even for the ICA-based methods.

In order to provide a quantitative study we com-

pute the root mean square error (RMSE):

RMSE =



−



(3)

where k.k denotes the Frobenius norm and S

the cen-

tered and normalized version of the original spectrum

used to construct the mixtures.

denotes either

the spectra estimated by ICA-based methods or the

centered and normalized versions of the spectra esti-

mated by NMF or MLPSS.

The values of RMSEs obtained for the estimated

spectra (see ﬁgure 3) are: 0.1605 for JADE, 0.1603

for FastICA, 0.8017 for NMF and 0.1264 for the

MLPSS algorithm. These values conﬁrm that ICA-

based methods give practically the same results and

that NMF fails to estimate this spectrum. Moreover,

we can conclude that the MLPSS method gives the

best estimate, which, additionally, has positivevalues.

In the following we consider the case where a lin-

ear noise N

, decorrelated from the interesting spec-

tra, is added to the observations. We have chosen here

a Gaussian noise for the sake of simplicity. This noise

also simulates slight deforming effects on the peaks of

parafﬁn that may remain after the preprocessing steps

in real cases. This study is done by varying the signal-

to-noise ratio (SNR):

SNR = 20log



∑

i=1



[dB] (4)

Note that the decomposition (2) does not com-

pletely remove the noise N

. After this step, a gain of

17dB is obtained for high values of SNR (i.e. SNR=

50dB). This gain linearly decreases with the SNR, a

gain of 6.5dB being obtained for a SNR= 2.5dB.

Figure 4 shows the evolutions of the RMSEs for

the estimated spectrum

with respect to the SNR.

These values are averaged over 4 independent realiza-

tions of the noise. The values obtained by the JADE

algorithm (represented by “ ”) are superposed on

those obtained for the FastICA (represented by “×”).

These evolutions conﬁrm the conclusion stated above

even if, punctually, the RMSE of the MLPSS is larger

than the ones obtained by ICA methods.

Although these results give the MLPSS as the best

separation method, it is interesting to study the errors

Figure 4: RMSEs of

with respect to the SNR: “” JADE,

“×” FastICA, “•” NMF, “” MLPSS.

of, for example, the estimator

of the third spectrum

of the parafﬁn. These errors are shown in Figure 5.

Figure 5: RMSEs of

with respect to the SNR: “” JADE,

“×” FastICA, “•” NMF, “” MLPSS.

The result obtained for the MLPSS method is due to

the fact that the same peak of the parafﬁn is extracted

by two estimators,

and

. For real applications

this effect can perturb the estimator of the biopsy, es-

pecially when the preprocessing does not completely

compensate the deforming effects.

3.4.2 Real Dataset

The study is done on a dataset composed of K = 1254

Raman spectra acquired on a parafﬁn-embedded skin

biopsy. Spectral data were recorded into N

= 990

points in the 650-1816 cm

−1

range by using a Labram

microspectrometer. The preprocessing techniques de-

veloped in (Gobinet et al., 2007) are ﬁrstly used in

order to improve the estimated spectra.

Figures 6, 7 and 8 show the results obtained by

the JADE, NMF and MLPSS algorithms. The results

of the FastICA being the same with those given by

JADE are not presented here. The same parameters

as in the simulated case were used. Some residual

peaks of parafﬁn, which sometimes are negative, are

present on spectra estimated by the JADE algorithm.

However, this technique provides positive mixing co-

efﬁcients. The spectrum of the biopsy estimated by

NMF contains more energetic residual peaks of the

parafﬁn than the JADE estimator, whereas the spectra

of the parafﬁn are not well estimated. Spectra esti-

mated by MLPSS are close to the JADE results, but

the same peak of the parafﬁn (1135 cm

−1

) is extracted

by two estimators as in the simulated case. Moreover,

the application of this algorithm on another parafﬁn-

embedded skin biopsy led to a wrong estimation of

spectra, contrary to JADE.

COMPARATIVE STUDY OF BLIND SOURCE SEPARATION METHODS FOR RAMAN SPECTRA - Application on

Numerical Dewaxing of Cutaneous Biopsies

353

Figure 6: Spectra estimated by JADE.

Figure 7: Spectra estimated by NMF.

Figure 8: Spectra estimated by MLPSS.

4 CONCLUSIONS

Four BSS methods were studied on simulated and real

datasets. Taking into account only the positivity, the

NMF fails to estimate the interesting spectra. The

positivity combined with the independence allows the

MLPSS method to provide a good estimator for the

biopsy, but artefacts are obtained for the parafﬁn for

which the same peak is extracted by more than one

estimator. Furthermore, the results obtained by this

method depend on the analyzed biopsy. ICA-based

methods give good estimators for all spectra, which

do not depend on the biopsies, and extract positive

mixing coefﬁcients. These last methods can thus be

employed as an efﬁcient tool for the extraction of Ra-

man spectra of chemical species and consequently for

a numerical dewaxing of biopsies. However, all these

methods allow to extract a unique spectrum of the

skin, which might be insufﬁcient for a classiﬁcation

purpose. Investigations are under way for the study of

a numerical dewaxing based on least square methods,

taking into account the Raman spectra of the paraﬁn

estimated on parafﬁn blocks.

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