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Abstract: Electrocardiogram (ECG) is an important biomedical signal for analysing electrical activity of the heart
during its contraction and expansion. Analysis of ECG becomes difficult if noise is augmented with the signal during
acquisition. During recent years, several denoising techniques were analysed within the field of signal processing. In
this paper, non-local means (NLM) filtering technique is explored for denoising the ECG signal and results are
developed using Matlab coding. Non local means (NLM) uses concept of self-similarity. Due to the nature of the
algorithm, the most favourable case for the NLM is the periodic case, like signals, a straight edge, curved edge, texture
images and a complete line of pixels with a similar configuration. The noisy ECG signals are synthesized by adding
pulse signals and are then denoised at different levels by optimizing various NLM parameters. The experimental results
showed that the proposed technique successfully denoised the noisy ECG signals by selecting appropriate input NLM
parameters. Finally, the power signal to noise ratio (PSNR) and mean square error (MSE) were also evaluated.
INTRODUCTION
Electrocardiogram (ECG) is a graphic recording of the
flow of electrical current through the heart and it shows
the medical state of heart. ECG contains important
pointers to different types of diseases afflicting the heart.
It is one of the important tools used by medical
practitioner to examine the pathological and physiological
condition of the heart. The electrocardiogram signals are
irregular in nature and occur randomly at different time
intervals during a day. This need for continuous
monitoring the ECG signals, which by nature are complex
to comprehend and hence there is a possibility of the
analyst missing vital information which can be crucial in
determining the nature of disease. Thus computer based
automated analysis is recommended for early and accurate
diagnosis (J. Moss et al, 1996). Fig. 1 shows the ECG with
respect time obtained during one complete cardiac cycle.
This cycle is repeated with every heartbeat. The Heart is a
very unique four-chambered pump and it has the ability to
create electrical impulses on its own without any outside
influences that provides the driving force for the
circulation of blood in whole body. The electrical impulse
begins at the pacemaker of heart, which we call the SA
node. Then the impulse travels through the atria to the AV
node, and then down through the ventricles, causing the
heart to beat in a rhythmic and predictable way. With each
heart beat the synchronized depolarization spreading
through the heart and establish field potentials over the
whole body. These potential differences can be detected
by electrodes placed on the body's surface. The pattern of
the ECG varies according to the electrodes position but
certain features are always present. These features were
labelled as PQRST by Einthoven. The ECG waveform can
be broken down into three important parts each denoting a
peak on the either side represented by P, QRS, T, each of
them represent a vital processes in the heart. The ECG
signal is typically in the range of 2 mV and requires a
recording bandwidth of 0.1 to 120 Hz. ECG system
contains 12 leads. Six Limb leads (Lead I, Lead II, Lead
III, aVr, aVL and aVf ) and six Precordials lead (V1, V2,
V3, V4, V5 and V6). Each limb lead shows information
about different areas of the left ventricle. Lead I, Lead II,
and Lead III are bipolar leads and aVr, aVL, aVf are
unipolar leads. Precordial leads also called chest leads and
they are unipolar leads. Unipolar leads use the heart’s
centre as negative pole. The ECG is acquired by a noninvasive
technique, i.e. placing electrodes at standardized
locations (between intercostals rib spaces of sternum) on the skin of the patient (P. E. McSharry et al, 2003). In case
of a disease afflicting the heart, the waves get distorted
according to the area which is not functioning normally.
The amplitude and duration of the P-QRS-T-U wave
contains useful information about the nature of disease
related to heart. In bradycardia, less P-QRS-T-U waves
occur in one minute recording than normal and in
tachycardia more P-QRS-T-U waves occur. U wave occur
in rare case, normally P-QRS-T waves occur. P wave
represent atrial depolarization, QRS represent both atrial
repolarisation and ventricles depolarization, and T wave
represents repolarisation of ventricles (J. Moss et al 1996)
II. NON LOCAL MEANS (NLM)
Non local means (NLM) filtering also knows as statistical
neighbourhood filter and was first introduced by (Buades
et al, 2005). Their work has attracted over 1000 citations
and many extensions of the original algorithm have been
proposed Non local means (NLM), uses concept of SelfSimilarity.
Due to the nature of the algorithm, the most
favourable case for the NLM is the periodic case, like
signals, a straight edge, curved edge, texture images and a
complete line of pixels with a similar configuration. The
objective of this filtering technique is to fix the problems
associated with local smoothing filters by calculating the
smoothed value as a weighted average of other values in
the time series based upon the similarity between the
neighbourhoods around the time series value. NLM is an
edge preserving denoising method. NLM filter consider
the average of pixels which have higher similarity, instead
of closer one. On the other hand, due to the computational
complexity, the similarity is not calculated between any
two pixels on the whole domain, but within a searching
window, hence the term is “non local” and not “global”.
In the non-local means algorithm, smoothed values are
given by
( , ) i j
j N
S w i j y
(1)
Where the weights are given by the function
2
2 1 2
( , )
i j
n
Y Y
Y
i
w i j e
z
(2)
Where vector Yi is an intensity value in the
neighbourhood, around yi
, |Yi −Yj| is the difference in
intensity values during the proposed interval, |Y| is the
sample size, and β is a parameter chosen by the analyst to
control the amount of smoothing. According to (Coup’s et
al. 2007), β varies between 0.0 and 1.0, with values of β
closer to 1.0 better for high levels of noise and values of β
closer to 0.5 better for lower levels of noise. (Duval et
al.2011) notes that neighbourhood pre-selection can
improve the results of the non-local means algorithm by
assigning a weight of 0 to the yj values that have
neighbourhoods that are too dissimilar to the
neighbourhood, Yi under consideration. Duval et al. uses a
pre-selection test based upon the norm of the difference
between neighbourhoods. A more complex preselection method is described by (Buades et al, 2005). We use
Duval et al.’s preselection test:
2
2 1 2
( , )
0 o th e rw ise
i j
n
Y Y
Y
i j
i
e Y Y T w i j
z
(3)
(Duval et al. 2011), suggests that values of T near 20 or 30
work well for 2D images. This threshold does make sense
for denoising time series. We will consider thresholds of
the type T = δ(maxYj−minYj)|Y|, where δ ∈ [0.0,1.0].
This threshold is a percentage of an approximation of the
maximum intensity interval distance. Duval et al.
recommends window sizes of 5x5 or 7x7 for 2D image
processing. As before, it is uncertain if these results
translate to 1D time series denoising. In this algorithm, the
analyst can control the amount of smoothing via β, the
preselection parameter δ, the window size, and the portion
of the time series that is compared.
III. METHODOLOGY
In this work, three ECG signals are synthesized by setting
and optimizing different parameters. For creating ECG
signals, time series elements are synthesized that contain
features similar to those in real world data. The proposed
noise removal method using non local means technique is
illustrated by a flow chart as in Fig. 2. The noisy signal
s(t) is synthesized as s(t)= x(t)+n(t) where x(t) is the
original ECG and n(t) is the noise signal. The added noise
signals are pulse signals with 5 dB, 10dB, 15dB, 20dB and
25dB signal power.
Here, we examine parameter selection for ECG denoising.
The key NLM parameters are the patch size, specified as a
half-width P (so LΔ = 2P + 1), the size of N(s), specified
as a half-width M, and the bandwidth λ. The bandwidth λ
is a key parameter that controls the amount of smoothing
applied. An overly small λ will cause noise fluctuations to
have too much influence in the weighting different patches
and resulting in insufficient averaging; an overly large λ
will cause dissimilar patches to appear similar, resulting in
blur. (Ville et al, 2011) used the sure criterion for
parameter selection and noted that for their test set, a good
overall choice of lambda is 0.5 σ, where σ is the noise
standard deviation. The patch half-width P selects the
scale on which patches are compared, and should
generally be similar to the size of features of interest. For
ECG signals, a reasonable choice for P is the half-width of
the high-amplitude “R” ECG complex. (Brian Tracey et al,
2012) say that increasing the neighbourhood half-width M
(resulting in a “less local” search) should lead to better
performance. However, a larger search window maps
directly to increased computation, even in the case of the
fast algorithms. For ECG denoising of the QRS complex,
setting M large enough to include multiple heartbeats
allows multiple QRS regions with potentially similar
morphology to be compared. Note that the shape of highamplitude
QRS regions is naturally protected, as
differences between even visually similar peaks are
typically large, resulting in low weights and thus little
smoothing of these regions.
IV. RESULT AND DISCUSSION
For simulations, ECG signals were synthesized by setting
and optimizing different parameters. For creating ECG
signal, time series elements were synthesized that contain
features similar to those in real world data. The pulse
signals with different SNR levels were added to achieve
target mean square error (MSE) and Power signal-to-noise
ratio (PSNR) levels. The testing was initiated by applying
the proposed algorithm to three original ECG100,
ECG101, and ECG102 signals. After that, signals with
5dB, 10dB, 15dB, 20dB and 25dB noise were introduced
into the original signals. The original ECG102 and the
denoised ECG102 signals are shown in figure 3 and figure
4 respectively
CONCLUSION
In this paper we have demonstrated non local means based
filtering algorithm to denoise the ECG signals, this
technique is effective but little time consuming. It is
possible to remove noise up to the satisfactory level
without reducing the actual signal strength by optimizing
NLM parameters. Our present work shows the effect of MSE and PSNR with respect to the different noise levels
that is the MSE increases and PSNR decreases when we
move from 5 dB level to 25 dB noise levels for all test
signals.