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The following manuscript was published in
Yung-Sheng Chen and Yu-Ching Hsu, A Simple Baseline Correction Method for
Raman Spectra, IAENG Transactions on Engineering Sciences - Special Issue for the
International Association of Engineers Conferences 2019 (Edited By: Sio-Iong Ao,
Haeng Kon Kim, Oscar Castillo, Alan Hoi-shou Chan and Hideki Katagiri), World
Scientific Publishing Co Pte Ltd, pp. 21-32, 2020.
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A Simple Baseline Correction Method for Raman Spectra
Yung-Sheng Chen∗and Yu-Ching Hsu
Department of Electrical Engineering, Yuan Ze University,
Chungli, Taoyuan 320, Taiwan, ROC
∗E-mail: eeyschen@saturn.yzu.edu.tw
Baseline shifts caused by a variety of factors depending on the type of spec-
troscopy are common degradation problems in Raman spectra. An effective
and efficient method is presented for the baseline correction of Raman spectra.
A kernel smoothing function is developed for the estimation of baseline, and a
negative signal filter is designed for the removal of negative impulse responses
caused from the spectroscopy. Results on the computer and instrument imple-
mentation confirm the feasibility of the proposed method.
Keywords: Raman spectra; Spectrometers; Spectroscopic instrumentation;
Spectroscopy.
1. Introduction
In applied sciences, a lot of natural phenomena can be observed and mea-
sured based on a proper instrument for further analyzing and studying.
For example, in order to read a color-band resistor (which is an often-used
electronic component), except for the use of multimeter measurement or hu-
man observation and calculation, it can also be read by a computer vision
based method. 1–3 For the multimeter, it is also a quite significant instru-
ment for sensing or measuring electronic parameters (e.g., voltage, current,
resistance) and is indispensable to the area of science and technology. How-
ever, reading an analog multimeter usually relies on human eyes and has
two obvious problems, i.e., inefficiency and easy fatigue, while a long time
of reading the analog multimeter is needed. This conducts us to develop a
computer vision approach for automatically reading the analog multimeter
in recent.4,5 From such a research trend of instrument, the signal processing
method to the instrument of Raman spectroscopy is similar to the reading
technique (such as the computer vision method) to the analog multimeter.
An effective and efficient baseline correction algorithm for Raman spectra
is thus addressed in this paper.
Raman spectroscopy is a well-established but significant technique for
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revealing the molecular fingerprints based on its vibrational information.
Due to the label-free and non-invasive property as well as convenient appli-
cation, Raman spectroscopy has been widely applied for material analysis, 6
biological investigation,7medical diagnosis, 8and so on. Baseline is a com-
mon degradation problem in Raman spectra and usually results from the
spurious background signal or instrument fluctuation. The problem of base-
line will severely result in the difficulty of quantitative or qualitative anal-
ysis of Raman spectra. To overcome such a problem, baseline correction is
a necessary step before performing the Raman spectra analysis and usually
classified into three main types of methods, i.e., smoothing spline fitting,
wavelet decomposition and integration, and least squares error modelling
(or divided into physically and mathematically motivated approaches). The
merits and disadvantages of those methods have been investigated and can
be found in the related literatures. 6,7,9 A well-known commercial software
tool, called Origin/OriginPro developed by OriginLab Corporation, 10 have
been widely used in the related application fields, where the peak analysis
is one of the major functions in this product and includes the baseline cor-
rection function being focused in our study. In recent, due to the progress
of micro Raman spectroscopy, e.g., Micro Raman Identify (MRI) spectrom-
eter,11 users usually need a friendly interface to fast correct the baseline
with only a few controllable parameters. To achieve such a goal, an effective
and efficient baseline correction algorithm is presented in this paper. The
partial work of this study has been presented in the IMECS 2019.12
The rest of this paper is organized as follows. In Section 2, an illustra-
tion of base line estimation and correction is given and the base line mod-
eling is introduced at first. Then a kernel smooth function and a so-called
negative signal removal are developed to construct our baseline correction
algorithm. Section 3 shows the experimental results, where the behaviour
of the parameters is also discussed. The conclusion and future work of this
paper is finally drawn in Section 4.
2. Proposed Approach
All the samples of Raman spectra used in this study are from the MRI
spectrometer. 11 Two samples are illustrated in Fig. 1, where the baseline
(red colour) is estimated by the proposed method. Note that the negative
impulse responses result from the MRI spectrometer can also be filtered
out by the proposed method as illustrated in Fig. 1(b). Their final base-
line correction results are shown respectively in Fig. 2. The details of the
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(a)
(b)
Fig. 1. Illustrations of the measured Raman spectrum and the baseline (red colour) es-
timated by the proposed algorithm. (a) Sample-1: Measured Raman spectrum including
the baseline. (b) Sample-2: Measured Raman spectrum including not only the baseline
but also the negative impulse responses.
presented algorithm will be described as follows.
2.1. Baseline removal modeling
Let fraw be the raw observed Raman spectrum having Ndata points.
Generally, the raw data fraw is composed of the true signal (s), the baseline
(b), as well as the noise (n). It can thus be modelled as
fraw =s+b+n(1)
Based on the quality of nowadays technology, the noise term ncan be
ignored since it has a little effect compared to the baseline. Therefore,
the signal scan be estimated by subtracting the baseline bfrom the raw
data fraw. In other words, the estimation of baseline is the main task for
extracting the signal s. Let fbaseline be the estimated baseline. Then the
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(a)
(a)
Fig. 2. Results of baseline correction by the proposed algorithm. (a) Baseline correction
result for the Raman spectrum given in Fig. 1(a). (b) Baseline correction result for the
Raman spectrum given in Fig. 1(b).
correct signal fcorrect can be expressed as
fcorrect =fraw −fbaseline (2)
2.2. Smooth function
From the characteristic of Raman spectra, the baseline can be regarded
as a stable component from the human visual inspection, which is used to
carry the signal. Therefore, the key function of estimating the baseline is
first developed in this study for finding the local minima of the raw data
and smoothing them as the SMOOTH function depicted in Fig. 3(a).
Here fin is the input signal, whereas the fmin and favg are the resultant
local minima and averaged information. Assume the i-th data point is to
be processed, the sliding window is defined as [i−W, i +W], where W
is a positive integer and controls the window size. The functional blocks
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(a)
(b)
Fig. 3. Signal flow of the proposed method. (a) SMOOTH function block diagram
with MIN,MEAN and AVG operations for finding useful local stationary information.
(b) Flowchart of removing the negative impulse responses, extracting the baseline, and
obtaining the baseline correction result.
(MIN,MEAN, and AVG) shown in Fig. 3(a) are formulated respectively
as follows.
MINW(i) = min
∀j∈[i−W,i+W]fin(j) (3)
MEANW(i) =
X
∀j∈[i−W,i+W]
MINW(j)
/(2W+ 1) (4)
MEAN4W(i) =
X
∀j∈[i−4W,i+4W]
MEANW(j)
/(8W+ 1) (5)
AVGW(i) = (MEANW(i) + MEAN4W(i)) /2 (6)
Here MINWcomputes the fundamental local minima for the input signal
and after the processing of MEANW, the smoothed local minima fmin
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can be obtained. However, in our study on the MRI spectrometer,11 some
negative impulse responses (possibly resulting from the sensor device or
the integrated mechanism) may occur during the signal acquisition as the
Sample-2 shown in Fig. 1(b). To filter out such an unwanted negative signal,
it is reasonable to provide a more smoother local minimum as a reference
for comparison. A more wider MEAN4Wfunction is thus performed on
the resultant signal from MEANWand then combined with MEANWby
AVGWto obtain the useful reference signal favg. As long as the mean
input signal is less than the reference, it can be replaced by the mean signal,
otherwise the original input signal is remained.
2.3. Negative signal removal
The function block of (NegSignal Filter)Win Fig. 3(b) performs such a
negative signal removal, which can be formulated as below.
fout(i) = fref(i), fin(i)< f ref(i)
fin(i),otherwise (7)
Here fin represents the resultant mean signal from the input signal fin,
and can be computed as the formula in Eq. (4) with Wwindows size. fref
is obtained by the same way. Since the negative impulse responses may
be large or small as illustrated in Fig. 1(b), (NegSignal Filter)Wcascad-
ing (SMOOTH) and (NegSignal Filter)W/3cascading (SMOOTH) are
adopted respectively for the removal of large and small negative signal as
depicted in Fig. 3(b). It can be regarded as a two-stage negative signal fil-
ter. Here the SMOOTH extracts continuously the useful fmin and favg
from the filtered signal obtained by the NegSignal Filter. In this case,
the final baseline is estimated and output fmin located at the middle right
of the signal flow given in Fig. 3(b). Note here that if there is not any neg-
ative impulse responses such a two-stage negative signal filter would not be
performed, the baseline can be directly output from the fmin of the first
SMOOTH function block.
2.4. Baseline correction algorithm
The whole signal flow of the proposed algorithm is depicted in Fig. 3(b). Let
Pbe a binary parameter to control a multiplexer (MUX), which outputs
the estimate baseline fbaseline that comes from the two-stage negative
signal filter (P= 1) or the first SMOOTH function block (P= 0). The
baseline correction result fcorrect can be further obtained by the Signal
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Subtraction function block. For the given Raman spectra shown in Fig. 1,
the estimated baselines (red colour) and their baseline correction results
shown in Fig. 2 demonstrate the feasibility of the proposed algorithm.
Table 1. Performances of the five samples from the
Micro Raman Identify (MRI) spectrometer11 using the
proposed algorithm.
Samples data size W P execution time
(ms)
Sample-1 1559 19 0 5
Sample-2 1979 15 1 15
Sample-3 1010 15 0 3
Sample-4 1014 15 0 3
Sample-5 1973 31 1 23
3. Result and Discussion
The algorithm is implemented in Microsoft R
Visual Studio R
C++ 2013
and run on a laptop with Intel R
CoreTM 2 Duo 1.8 GHz CPU and 4G RAM.
In addition to the baseline correction results of Sample-1 and Sample-2
shown in Fig. 2, the results of other three samples are also given in Fig. 4 for
further evaluations. Fig. 4(a) shows our method can estimate effectively the
baseline for a background spectrum (Sample-3). Fig. 4(b) shows the result
of a material measured under such a background (Sample-4). Fig. 4(c)
shows the baseline estimation result for a spectrum with some negative
impulse responses corrupted, and its baseline correction result is shown in
Fig. 4(d) (Sample-5). The performances reported in Table 1 are evaluated
by using data size, W,P, as well as execution time (with milliseconds or
ms), where parameters Wand Pcan be selected by user. It can be observed
that the execution time of the presented method is positively related to the
data size and the window size W.
Before concluding this paper, the behaviours of Wand Pare briefly
discussed as follows. Considering the Sample-1, the results of baseline es-
timation using parameter (a) W= 7, (b) W= 9, and (c) W= 31 are
shown in Fig. 5. By comparing the result using W= 19 shown in Fig. 1(a),
it can be observed that the small W(see Fig. 5(a) and 5(b)) will result
in an under-fitting, whereas the large W(see Fig. 5(c)) will result in an
over-fitting. Since there are possibly a lot of various Raman spectra, it is
reasonable to select a proper Wby means of heuristic manner. Considering
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(a)
(b)
(c)
Fig. 4. Results of the other samples for baseline correction. (a) The estimated baseline
fits well for a background spectrum. (b) Result of a material measured under such a
background in (a). (c) The estimated baseline for a spectrum with some negative impulse
responses corrupted. (d) The final baseline correction result for the spectrum in (c).
the Sample-2, with the same W= 15 and set P= 0, it can be observed
that the baseline estimation is influenced with the negative impulse signal
as the result shown in Fig. 6 by comparing the result given in Fig. 1(b),
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(d)
Fig. 4. (Continued.)
where the negative signal is removed by setting P= 1.
Based on our experiments, the effectiveness and efficiency of the pro-
posed baseline correction algorithm for Raman spectra have been confirmed.
As a result, in accordance with the desired application of micro Raman
spectroscopy, e.g., Micro Raman Identify (MRI) spectrometer, 11 the goal
of providing users a friendly interface to fast correct the baseline with only a
few controllable parameters has been achieved by the presenting approach.
4. Conclusion and Future Work
In the field of Raman spectrometer, it is of great importance to correct the
baseline before performing the quantitative and qualitative analysis for a
raw Raman spectrum. The presented algorithm can effectively not only
correct the baseline but also remove the negative impulse responses. The
execution time with milliseconds performs the efficiency of the proposed
method. This algorithm has been implemented in the instrument software
of Micro Raman Identify (MRI) spectrometer11 and thus confirms its fea-
sibility in the engineering and laboratory application. Because the peak
fitting or peak decomposition is also a significant function in the field of
peak analysis, it could be a good topic along this study direction and re-
garded as our future work.
Acknowledgment
This work was supported in part by the Protrustech (Taiwan), which is a
professional instrument company, working on Raman spectroscopy, Photo-
luminescence, Photo-reflectance, and so on.
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(a)
(b)
(c)
Fig. 5. Results for Sample-1 with the parameter: (a) W= 7 (sever under-fitting), (b)
W= 11 (little under-fitting), (c) W= 31 (over-fitting).
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