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A significant feature of the coming digital era is the exponential increase in digital data, obtained from various signals specially the biomedical signals such as electrocardiogram (ECG), electroencephalogram (EEG), electromyogram (EMG) etc. How to transmit or store these signals efficiently becomes the most important issue. A digital compression technique is often used to solve this problem. This paper proposed a comparative study of transform based approach for ECG signal compression. Adaptive threshold is used on the transformed coefficients. The algorithm is tested for 10 different records from MIT-BIH arrhythmia database and obtained percentage root mean difference as around 0.528 to 0.584% for compression ratio of 18.963:1 to 23.011:1 for DWT. Among DFT, DCT and DWT techniques, DWT has been proven to be very efficient for ECG signal coding. Further improvement in the CR is possible by efficient entropy coding.
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ACEEE Int. J. on Signal & Image Processing, Vol. 01, No. 03, Dec 2010
An Optimized Transform for ECG Signal
Compression
Mrs.S.O.Rajankar1, Dr. S.N. Talbar2
1
Sinhgad College of Engineering, Pune, India.
Email: supriya.rajankar@gmail.com
2
S.G.G. S. College of Engineering and Technology, Nanded, India.
Email: sntalbar@yahoo.com
Abstract-A significant feature of the coming digital era is the samples where inter-beat and, intra-beat correlation is
exponential increase in digital data, obtained from various exploited. Some of the DDC algorithms are Turning point
signals specially the biomedical signals such as (TP), Amplitude zone time epoch coding (AZTEC), Co-
electrocardiogram (ECG), electroencephalogram (EEG), ordinate reduction time encoding system (CORTES), Scan
electromyogram (EMG) etc. How to transmit or store these
signals efficiently becomes the most important issue. A digital
along polynomial approximation (SAPA), and Non
compression technique is often used to solve this problem. redundant template. These algorithms suffer from
This paper proposed a comparative study of transform based sensitiveness to sampling rate, quantization levels and high
approach for ECG signal compression. Adaptive threshold is frequency interference. It fails to achieve high data rate
used on the transformed coefficients. The algorithm is tested along with preservation of clinical information [10]. In
for 10 different records from MIT-BIH arrhythmia database Transform based technique compressions are accomplished
and obtained percentage root mean difference as around by applying an invertible orthogonal transform to the
0.528 to 0.584% for compression ratio of 18.963:1 to 23.011:1 signal. Due to its de-correlation and energy compaction
for DWT. Among DFT, DCT and DWT techniques, DWT has properties the transform based methods achieve better
been proven to be very efficient for ECG signal coding.
Further improvement in the CR is possible by efficient
compression ratios. The commonly used transforms for
entropy coding. data compression are DCT, DST, DFT and DWT. In
parameter extraction methods a set of model
Index Terms: Electrocardiogram (ECG), Discrete Fourier parameters/features are extracted from the original signal
Transform (DFT), Discrete Cosines Transform (DCT), (model based) which involves methods like Linear term
Discrete Wavelet Transform (DWT) etc. prediction LTP) and analysis by synthesis (ASEC) [5],
[10].
I. INTRODUCTION In this paper different transform like DCT, DFT and
DWT are studied for ECG signal compression. A threshold
The ECG is a one of the important physiological signal
which depicts the electrical activity of a heart. ECG based algorithm is proposed to achieve better compression.
processing is a topic of great interest in the scientific
community because based on the ECG’s a diagnosis is II. TRANSFORM TECHNIQUES
done for detecting abnormalities in the heart functioning A. Discrete Fourier Transform
[7]. The amount of ECG data grows with the increase of Discrete Fourier Transform is a fundamental transform
number of channels, sampling rate, sample resolution, in digital signal processing with applications in frequency
recording time, etc. As an example, with a sampling rate of analysis, signal processing etc. The periodicity and
360 Hz, 11 bits/sample data resolution, a 24-h record symmetry properties of DFT are useful for compression.
requires about 43 Mbytes per channel[5],[6]. Therefore an The uth DFT coefficient of length N sequence {f(x)} is
effective data compression scheme for ECG signal is defined as in “(1)”:
required in many practical applications such as ECG data
storage, ambulatory recording systems and ECG data N −1
transmission over telephone line or digital F (u ) = ∑ f ( x)e− j 2π ux / N u = 0,1,.... N − 1 (1)
telecommunication network for telemedicine. The main x =0
goal of electrocardiogram (ECG) data compression
techniques is to preserve the most useful diagnostic And its inverse transform (IDFT) as in “(2)”:
information while compressing a signal to an acceptable
size. Lossless compression is the best choice as long as the N −1
1
compression ratio is acceptable, but it cannot usually offer f ( x) =
N
∑ F (u )e
u =0
j 2π ux / N
x = 0,1,....., N − 1 (2)
a satisfactory compression ratio (CR). To obtain significant
signal compression, lossy compression is preferable to a
The number of complex multiplications and additions to
lossless compression.
compute DFT is N2. Moreover fast algorithms exist that
ECG data compression algorithms can be categorized as
makes it possible to compute DFT efficiently [9]. This
direct data compression (DDC), Transform based and
algorithm is popularly known as Fast Fourier Transform
Parameter extraction. Direct data compression is a time
(FFT) which reduces the computations to N log2N.
domain compression algorithm which directly analyses
©2010 ACEEE 33
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ACEEE Int. J. on Signal & Image Processing, Vol. 01, No. 03, Dec 2010
B. Discrete Cosine Transform This multi-resolution wavelet algorithm decomposes a
Discrete Cosine Transform is a basis for many signal signal f(t)with the help of φ (t ) and wavelet function
and image compression algorithms due to its high de- byψ (t).These functions together resolves the signal into its
correlation and energy compaction property. A discrete coarse and detail components[8],[10]. Thus using multi-
Cosine Transform of N sample is defined as in”(3)”: resolution idea, the signal f(t)is defined in terms of scale
and wavelet coefficients, c(k) and d(k), respectively. That
2 N −1
π (2 x + 1)u
C (u )∑ f ( x) cos[
is,
F (u ) = ]
N x =0 2N ∞ ∞ ∞
u = 0,1,..., N − 1, (3)
f (t ) = ∑
k =−∞
c(k )φk (t ) + ∑ ∑ d ( j, k )ψ
j = 0 k =−∞
j ,k (t )
(8)
1
Where C(u) = for u=0 The first summation gives a function that is a low
2 resolution or a coarse approximation of f (t); the second one
represents the higher or finer resolution to give detailed
= 1, otherwise. information of the signal.
The function f(x) represents the value of xth samples of
III. PERFORMANCE MEASUREMENT
input signals. F(u) represents a DCT coefficients. The
inverse DCT is defined in similar fashion as follows in The evaluation of performance for testing ECG
“(4)”: compression algorithms includes three components:
compression efficiency, reconstruction error and
2 N −1 π (2 x + 1) u computational complexity. The compression efficiency is
f ( x) = ∑ C ( u ) F ( u ) cos[ 2 N ]
N u =0
given by compression ratio (CR). The compression ratio
and the reconstruction error are usually dependent on each
x = 0,1, ..., N − 1. (4)
other. The computational complexity component is part of
the practical implementation consideration [6], [8].
Since DCT belongs to family of DFT there are Fast
A. Compression Measurement
DCT algorithms of computational complexity N log2N
similar to FFT[9]. All data compression algorithms minimizes data storage
by reducing the redundancy wherever possible, thereby
C. Discrete Wavelet Transform increasing the compression ratio. The compression ratio
Wavelet transforms have become an attractive and (CR) is defined as the ratio of the number of bits
efficient tool in many applications especially in coding and representing the original signal to the number of bits
compression of signals because of multi-resolution and required to store the compressed signal. A high
high-energy compaction properties. Wavelets allow both compression ratio is typically desired. A data compression
time and frequency analysis of signals simultaneously algorithm must also represent the data with acceptable
because of the fact that energy of wavelet is concentrated in fidelity while achieving high CR.
time and still possesses the wave like characteristics. As a
result wavelet representation provides a versatile boriginal
mathematical tool to analyze transients, non-stationary CR =
bcompressed
signals. Wavelets ψ a ,b (t ) are functions generated by one (9)
single basis function, called mother wavelet ψ (t) by
B. Distortion Measurement
dilation ‘a’ and translation ‘b’ represented as in”(5)”:
One of the most difficult problems in ECG compression
1 ⎛ t −b ⎞ and reconstruction is defining the error criterion that
ψ a ,b (t ) = ψ⎜ ⎟ measures the ability of the reconstructed signal to preserve
|a| ⎝ a ⎠ (5) the relevant information. Different objective error measures
namely; root mean square error (RMSE), percentage root
If a and b are discredited then discrete wavelets can be mean difference (PRD), signal to noise ratio (SNR) are
represented as in”(6)”: used for calculation of reconstruction error. Among these
error measures, the ECG processing is frequently measured
ψ j ,k (t ) = a0 j /2ψ (a0 j t − kb0 )
− −
by the percentage root mean difference (PRD). It is most
(6)
commonly defined as:
where for dyadic sampling a0=2 and b0=1.
∑
2
⎡ x ( n) − x ( n) ⎤
N
n =1 ⎣ ⎦ ×100
ψ j ,k (t ) = 2 ψ (2 t − k )
− j /2 −j
j, k ∈ Z PRD =
∑ n=1 x(n)
(7) N 2
(10)
©2010 ACEEE 34
DOI: 01.IJSIP.01.03.224
ACEEE Int. J. on Signal & Image Processing, Vol. 01, No. 03, Dec 2010
where x(n) and x ( n) are the values of the original and waveform of the ECG signal. The CR and PRD values
increases proportionally if the percentage threshold is
reconstructed samples, respectively, and N is the length of increased as in “fig.2” and “fig.3”.The energy compaction
the window over which the PRD is calculated. The PRD ability for different transform is shown in “fig.4”. With
indicates reconstruction fidelity by point wise comparison 4096 samples, for DFT method the PRD is around 0.222
with the original data. Despite their wide use, PRD do not to 1.020% with the corresponding CR 4.362:1 to
indicate precisely the quality of signal's reconstruction and 15.814:1.For DCT the PRD is around 0.181 to 0.9346%
the decompressed signal has to be evaluated by visual with CR 5.446:1 to 19.23:1.In case of DWT the PRD is
inspection also. around 0.214 to 0.584% with the CR 9.315:1 to 23.011:1.
The “fig.5” explains about effect of number of samples on
IV. CODING ALGORITHM CR.
Transform based techniques because of their high 1400
compression ability have gained popularity. In this method 1200
the preprocessed signal is transformed to get the de- 1000
correlated coefficients. The thresholding or quantization of 800
transformed coefficients gives the actual compression, 600
0 500 1000 1500 2000 2500 3000 3500 4000
which is lossy one. But it has good performance and low (a)
computational cost. In this paper the comparative study of 1400
DFT, DCT and DWT is carried out. Following are some 1200
important steps of the proposed algorithm. 1000
• Transform the ECG signal using DFT/DCT/DWT. 800
• To achieve an adaptive threshold compute the 600
0 500 1000 1500 2000 2500 3000 3500 4000
maximum value of the transformed coefficients. (b)
• Apply the threshold of a fix percentage based on
absolute maximum values of the transform Figure 1. (a) Original and (b) Reconstructed signal of record number 207
coefficients. with DWT (PRD=0.584% and CR=23.011:1)
• After threshold operation to reconstruct the signal 25
apply inverse transform.
For wavelet based compression the signal is
20
decomposed up to fifth level using Bior4.4 wavelet. Bi-
orthogonal wavelets also allow perfect reconstruction of
Compression ratio
15
the signal using linear phase filter banks which in turn
avoid reconstruction error at the beginning and at the end
of the signal. 10
DFT
DCT
DWT
V. EXPERIMENTAL RESULTS 5
The data from MIT-BIH arrhythmia database is used to
0
test the performance of the coding schemes. This database 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
% Threshold
is sampled at 360Hz, and the resolution of each sample is
11 bits/samples. The algorithm is tested for 1024, 2048 &
Figure 2. Comparison of CR for different transforms
4096 samples of the record numbers 100, 103, 105, 107, (record number 207).
111, 200, 203, 205, 207 and 210. Table I summarizes the
results for record number 207 with maximum
threshold.”Fig.1” shows original and reconstructed
TABLE I.
PERFORMANCE RESULTS FOR DIFFERENT TRANSFORM METHODS FOR RECORD NUMBER 207 WITH MAXIMUM THRESHOLD
Number of DFT DCT DWT
samples CR PRD CR PRD CR PRD
1024 10.343 0.405 12.337 0.172 18.963 0.528
2048 11.702 0.683 14.027 0.623 21.558 0.561
4096 15.815 1.021 19.230 0.935 23.011 0.584
©2010 ACEEE 35
DOI: 01.IJSIP.01.03.224
ACEEE Int. J. on Signal & Image Processing, Vol. 01, No. 03, Dec 2010
1.4
CONCLUSION
1.2
For the transforms considered in this paper as the
DFT
Percentage Root Mean Diffrence DCT
percentage threshold is increased the number of
1 DWT transformed coefficients with zero value gets increased
0.8
which improves the CR but PRD also gets increased
proportionally. As the PRD indicates reconstruction fidelity
0.6 the increase in its value is actually undesirable. In
0.4
comparison with DFT and DCT the rise in PRD for DWT
is less but CR is more, also energy compaction in DWT
0.2 more. So the DWT is found to be more suitable for ECG
0
signals compression. Also it is observed that as the number
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
% Threshold of samples is increased the correlation among the samples
and hence the CR is increased. It is possible to further
Figure 3. Comparison of PRD for different transforms increase the CR by using effective coding methods.
( record number 207).
REFERENCES
100.002
[1] Abo-Zahhad, M. and Rajoub B.A., “An effective coding
100
technique for the compression of one-dimensional signals
99.998
using wavelets”, Medical Engineering and Physics, 2002, 24,
pp.185–199.
% Energy retained
99.996 [2] Leonardo Vidal Batista Elmar Uwe Kurt Melcher a, Luis
Carlos Carvalho b, “Compression of ECG signals by
99.994 optimized quantization of discrete cosine transform
coefficients”, Medical Engineering & Physics, 2001, 23, pp.
99.992 DFT
DCT 127–134.
DWT [3] Gholam-Hosseini, H., Nazeran, H. and Moran, B., “ECG
99.99
compression: evaluation of FFT, DCT, and WT
99.988 performance”.Australasian Physical & Engineering Sciences
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
% Threshold in Medicine,1998, 21, pp. 186–192.
Figure 4. Comparison of % energy retained for different transforms [4] Jalaleddine SMS, Hutchens CG, Strattan R D, Coberly W
(record number 207) A., “ECG data compression technique-a unified approach”,
IEEE transactions on Biomedical Eng 1990,37(4),pp.329-43
25 [5] Julian Cardenas-Barrera, Juan valentine Lorenzo-Ginori,
“Mean-Shape vector quantizer for ECG Signal Compression”,
20 IEEE transactions on Biomedical Eng 1999, 46(1), pp. 62-70.
[6] Shang-Gang Miaou,Heng-Lin Yen, Chih-Lung Lin, “Wavelet-
Based ECG Compression Using Dynamic Vector
Compression ratio
15
Quantization with Tree Code vectors in Single Codebook”,
IEEE transactions on Biomedical Eng 2002, 49(7), pp. 671-
10 680.
1024 samples
2048 samples [7] W. J. Tompkins and J.G. Webster, “Biomedical Digital Signal
4096 samples
5
processing” PHI-2006.
[8] R.shanta selva Kumari, V Sadasivam, “A novel algorithm for
wavelet based ECG signal coding”, Science Direct Computers
0
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 and Electrical Engineering, 2007, (33), pp. 186-194.
% Threshold
[9] Tinku Acharya and Ajoy K.Roy, “Image Processing Principles
Figure 5. Comparison of CR for different number of samples with DWT and Applications”, John Wiley.
(record number 207) [10] M. Sabarimalai Manikandan, S. Dandpat, “ Wavelet
Threshold based ECG compression using USZZQ and
Huffman coding of DSM”, Science Direct Biomedical Signal
Processing and Control 2006, pp. 261-270.
©2010 ACEEE 36
DOI: 01.IJSIP.01.03.224
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