# Baseline Wandering Removal from Human Electrocardiogram Signal

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```					International Journal of Electrical & Computer Sciences IJECS/IJENS Vol: 9 No: 9                         - 11 -

Baseline Wandering Removal from Human Electrocardiogram
Signal using Projection Pursuit Gradient Ascent Algorithm

Zahoor-uddin
Assistant Professor
Email: zahooruddin79@yahoo.com

Farooq Alam Orakzai
Assistant Professor
Email: farooqorakzai@hotmail.com

Department of Electrical Engineering
CIIT, Quaid Avenue, Wah Cantt,
Pakistan
Phone# 092-51-9272614

Abstract-Baseline       noise      removal         from   orthogonal projection of the signal mixtures. Now
electrocardiogram (ECG) signal is a blind source          the key point is this that how we can calculate such
separation problem. Various noises affect the             a weight vector. In projection pursuit one signal is
measured ECG signal. Major ECG noises are                 extracted at a time which will be as non Gaussian
baseline noise, electrode contact noise, muscle noise,    as possible. This method does not need to extract
instrument noise. Baseline noise distorts the low
frequency segment of ECG signal. The low frequency
all signals from mixture signals. We can extract
segment is s-t segment. This segment is very              any number of possible mixing signals [2]. In case
important and has the information related to heart        of our problem we have two signals one is ECG
attack. People apply various algorithms to remove         signal and other one is baseline noise signal. Let
this noise from noisy ECG signal. We have applied         ECG signal is denoted by s1 and baseline noise
projection pursuit gradient ascent algorithm to
by s2 , now the mixture signal can be represented
remove this noise from the measured ECG signal.
This algorithm separates the independent signals          as,
from a mixture of signals. Efficient removal of                         pi = ai s1 + bi s2    (1)
baseline noise might give us certain information that
are hidden from the doctors until now which may
save the life of a person. Results for different          Where pi are the mixtures, ai and bi are some
baseline noise signals were analyzed. Different signal    real coefficients. In real life problems we have only
from MIT-BIH database were also analyzed for error         pi , mixing signals s1 and s2 are always unknown.
in term of standard deviation and mean of error
signal. Finally we did a comparative study of the
The basic job is to separate the component signals
results of different algorithms like kalman filter,        s1 and s2 from the mixture signals pi . Kurtosis
cubic spline and moving average algorithms and            was used as a measure of non gaussianity to
showed that projection pursuit is the efficient one.      separate the component signals from the mixture.
Kurtosis have no information about the Gaussian
Keywords: Baseline Noise, Cubic spline,                   random variable. It has a positive value for peaked
Electrocardiogram, heart attack, Kalman filter,           activity distribution and negative value for flat
projection pursuit.                                       activity distribution. Kurtosis for a unit variance
variable can be calculated by the following
I. INTRODUCTION                           equation,
Projection pursuit gradient ascent is a blind source
separation method. The source signals must have                     kurt ( y ) = E{( y 4 )} − 3   (2)
non Gaussian probability density functions and
they must be statistically independent [1]. Mixture
signals tends toward gaussianity which can be seen        Gradient ascent algorithm requires             some
from central limit theorem. Here each source signal       preprocessing steps.
is extracted from a set of mixtures signal by             (1) Centering the available mixed data
calculating inner product which gives an

192091 IJECS-IJENS @ International Journals of Engineering and Sciences IJENS
International Journal of Electrical & Computer Sciences IJECS/IJENS Vol: 9 No: 9                              - 12 -

pi = pi − ui                          will be maximum when y = s, also kurtosis of the
extracted signal y to be maximal when w is
(2) This second step which simplifies the problem       orthogonal to the projected axis. Projection pursuit
of estimation to a certain extent is whitening or       extract estimated source signals in a stepwise
sphering. This linearly transform the data, where       manner from mixture signals using gram-Schmidt
the transformed data vectors are uncorrelated and       orthogonalization, where estimated source signals
having variance one. Sphering can be done by            are Y = ( y1 , y2 ,......., ym )T and signal mixtures
using singular value decomposition (SVD). If we         are Q = (q1 , q2 ,......., qm )T . We will apply repeated
have a matrix of mixture signals in the form of M
cycles of extraction of a signal yi , and then we will
by N array of M mixtures having N values in each
mixture. SVD can be applied in a standard form as,      subtract that signal from the signal mixtures to get
signal mixtures without that extracted signal. Let
p = UDV T                  (3)     we             have                original        signal
mixture Q = (q1 , q2 ,......., qm )T , after getting a
Where U is a matrix of Eigen vectors, V is an array     weight vector w1 we will get a signal y1 = w1T Q .
of Eigen vectors and D is an N by N diagonal            We will subtract y1 from mixture signals and will
matrix of singular values. Here U contains
get the new mixtures as follows,
Eigenvectors which are orthogonal to each other
that is why they are uncorrelated. All the vectors of
U are basically signal mixtures which are                                          E[ y1Qi ] y1
Qi (−1) = Qi −                        (5)
uncorrelated and orthogonal. We know that SVD                                       E[ y12 ]
provides vectors of the unit length while our
requirements are unit variance also. Thus dividing      After estimating y2 we can write,
each vector by its variance will result in a vector
having unit variance.
E[ y2 Qi (−1)] y2
Qi (−2) = Qi (−1) −                             (6)
ui                                                           E[ y2 2 ]
ui =
E{ui 2 }

Let assume that Q=U, where Q is a set of sphere         An important point here is that this each extracted
data.                                                   signal y is orthogonal to every mixture signal
The main steps of the algorithm are summarized as       extracted up till now. So for y1 we can
follows [3] ,                                           write E[Qi (−1) y1 ] = 0 , for i = 1,......, M . Thus we
(1) center the available mixed data                will repeat this extract and subtract procedure until
(2) sphering of the data                           separate the M th signal from the mixed data.
(3) select a weight vector w of unit norm
(4) update      the     weight      vector by
wnew = wold − η E[Q( wold Q) Q]
T   3                         II. RESULTS AND DISCUSSION
Baseline noise occurs due to respiratory signal and
(5) normalize the updated vector to unit
body movements. Respiratory signal wanders
length,
between 0.15Hz and 0.3Hz frequencies [4]. Body
(6)
movements are time varying signals that occur at a
w
wnew = nwe                         certain instant of time and then disappear. This
wnew
baseline noise separation from ECG is a blind
source separation problem. We apply a blind
(7) repeat the process until end                   source separation technique, projection pursuit
First, maximize the kurtosis of the mixture signals     gradient ascent method. This method sequentially
and then extracting the signal by the following         extracts signals from the mixed data. An ECG
equation                                                signal was found at [5] which is noise free signal, a
plot of which is shown in figure 1 bellow.
yi = wiT Q                (4)

Step by step extraction can be done when one
want to extract more than one signals. For super
Gaussian signal kurtosis of the extracted signal y

192091 IJECS-IJENS @ International Journals of Engineering and Sciences IJENS
International Journal of Electrical & Computer Sciences IJECS/IJENS Vol: 9 No: 9                                  - 13 -

table 4. Then the results for kalman filter, moving
average and cubic spline technique were studied
from [4]. The combined results of projection
pursuit, Kalman filter, cubic spline and moving
average are shown in table 3.
Table. 3
Algorithm             Error mean       Error STD.
Figure. 1 A pure ECG signal               Projection pursuit         -0.0034              0.0068
Kalman filter             0.073               0.076
where more noise signals exist. One of them is             Cubic spline              1.010               3.666
shown in figure 2.
The level of distortion is minimum for projection
pursuit which is shown in table 3. Thus, it has been
concluded that projection pursuit is the best choice
among these algorithms for baseline noise removal.
Table. 4
Records          Age        Sex        Error         Error
STD          Mean
S0010_re.dat          81     female     0.0194        0.0129
Figure.2 Baseline noise signal               S0015lre.dat          58     female     0.0194       -0.0129
S0017lre.dat          63      Male      0.0050       -0.0055

After mixing the two signals and applying the
algorithm results are summarized in table 1.                           III. CONCLUSION
Now considering another type of baseline noise         Projection pursuit is an efficient way of separating
signal shown in figure 3. After getting mixed data     signals from a mixture where mixing signals are
and after applying the algorithm the results are       non Gaussian and independent. The results of this
given in table 2.                                      algorithm are very effective in terms of standard
deviation and mean of the error signal when
compared to the results of the other algorithms.
One disadvantage of this algorithm is that it
extracts one signal at a time, while ICA extracts all
the mixing signals at same time.

IV. REFERENCES
Figure.3 Baseline noise signal              [1]A. Hyva¨rinen, E. Oja, “Independent component
analysis: algorithms and applications.” Neural
gnal                      Networks, vol. 13, pp. 411-430, 2000
Table.1
[2] Friedman, JH, & JW, Turkey, “A projection
Mean               STD                      pursuit algorithm for exploratory data
analysis,” IEEE transaction on computers, vol
-2.4667e-004            0.0223                   29, pp 881-890, 1974
[3] James V.Stone, “independent component
Table.2                                                analysis.” A tutorial, 2004.
Mean               STD                  [4] MA Mneimneh, Eeyaz, “An adaptive kalman
filter for removing baseline wandering in ecg
-1.0077e-004            0.0110                    signal”, Computers in Cardiology, vol. 33,
pp.253−256, 2006.
[5]http://eleceng.dit.ie/tburke/biomed/assignment
Kurtosis is not a good estimator for supper               1. html
Gaussian data. I is suitable for sub Gaussian data.    [6]www.mit.edu/~gari\CODE\Noise\Noise
I analyzed the results obtained from the algorithm         Generator tools.htm
for different signals obtained from PTB Diagnostic     [7]Physikalisch-Technische Bundesanstalt (PTB)
ECG Database [7] in terms of mean and standard             Diagnostic ECG Database is available at:
deviation of the error signal which are shown in        http://www.physionet.org/physiobank/database/

192091 IJECS-IJENS @ International Journals of Engineering and Sciences IJENS

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