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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 DOI: 01.IJSIP.01.03.224 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