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Digital Signal Processing 18 (2008) 900–906

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Digital Signal Processing www.elsevier.com/locate/dsp

Pre-processing deconvolution based technique for improving the performances of ECG codecs: Comparison to SPIHT Lina El Khansa, Amine Nait-Ali ∗ , Mohamad Khalil Université Paris XII—Val de Marne, 61, Avenue du Général de Gaulle, Créteil, France

a r t i c l e

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Article history: Available online 23 April 2008 Keywords: ECG compression Deconvolution Regularization SPIHT Encoding/decoding

a b s t r a c t In this paper, a deconvolution preprocessing module for ECG codec performance improvement (DPM-ECPI) is presented. The idea is simple but efficient. Primary, it consists in transforming an ECG signal to an impulsional one using a deconvolution process. The obtained signal is then encoded for either transmission or storage. In this work we take into consideration the well known SPIHT algorithm, used also for efficient comparison purpose. To reconstruct the signal, a simple convolution is however applied to the decoded impulsional signal. For high compression ratios, we show that this new compression scheme is particularly interesting than a direct coding. As it is common, real signals from MIT-BIH arrhythmia database have been used to validate the proposed scheme. © 2008 Elsevier Inc. All rights reserved.

1. Introduction Electrocardiography deals with the electrical activity of the heart; ECG is a record of the origin and the propagation of the electrical potential through cardiac muscles. It is considered a representative signal of cardiac physiology useful in diagnosing cardiac disorders. The state of cardiac heart is generally reflected in the shape of ECG waveform and heart rate. It may contain important pointers to the nature of diseases afflicting the heart. However, bio signals being non stationary signals, the reflection may occur at random in the time scale, therefore for effective diagnostics, the study of ECG pattern and heart rate variability signal may have to be carried out over several hours. Thus, the volume of the data being enormous, the study is tedious and time consuming. That is why, nowadays, storage and transmission of digital ECG signals are of great importance for various medical applications, mainly in telemedicine [1,2]. Commonly, lossy ECG compression techniques are classified into three main categories. The first category is generally called the direct method one. However, in this class, the ECG is simply compressed in time domain [3,4]. The second category concerns the transformation methods where the original samples are transformed and the compression is performed in a new representation domain. Among the transform-based techniques, several algorithms based either on discrete cosine transform (DCT) [5] or discrete wavelet transform (DWT) [6–9] have been successfully used in this field. Finally, the last category consists in extracting the useful parameters from the ECG signal. These parameters are required a posteriori for the reconstruction purpose [10–12]. In the present paper, the goal does not consist in proposing a new codec, but we aim to reveal how one can increase its performance just by adding to the compression scheme an efficient pre-processing module (PM). However, as we will see later, including a deconvolution technique in the PM will significantly increase the compression ratio (CR) for a given signal

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Corresponding author. E-mail address: [email protected] (A. Nait-Ali).

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L. El Khansa et al. / Digital Signal Processing 18 (2008) 900–906

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quality. In fact, the approach consists in encoding an impulsional signal corresponding to an ECG instead the common direct encoding. The set partitioning in hierarchical trees (SPIHT) will be used in this work as a reference codec. Consequently, the present paper is organized as follows. In Section 2, we present a brief review to evoke both the deconvolution principle and the SPIHT algorithm. The proposed algorithm is afterwards detailed in Section 3. The results obtained from widespread real ECG signals are presented and commented in Section 4. At last, a conclusion of this work is drawn in Section 5. 2. Short review Since the DPM-ECPI includes the deconvolution technique for the pre-processing phase, we briefly describe the most common theory in Section 2.1; whereas in Section 2.2, the well-known SPIHT codec will be evoked. 2.1. Linear deconvolution principle In linear time invariant systems, output y (t ) is related to input x(t ) through the convolution with the system impulse response, y (t ) = h(t )x(t ).

(1)

A common identification problem is finding a good estimate of h(t ) from the knowledge of x(t ) and y (t ) which requires a deconvolution process. The deconvolution problem is mathematically classified as an ill-posed problem [13,14]. Let us consider the following linear model: y = Hx + n,

(2)

where x is the input signal vector (to be estimated), y is the output signal vector (considered known, since it represents the observed data), H is a Toeplitz matrix corresponding to a linear system (considered also known), n is a zero-mean Gaussian noise vector. The estimated vector xˆ is estimated by minimizing the following least square criterion:





xˆ = argmin Q MCR (x) ,

(3)

where (3) Q MCR (x) = y − Hx2 + μx2

(4)

and μ is a regularization parameter. We will explain later how this parameter is chosen. Minimizing (4) means requires that ∂ Q /∂ x = 0 which implies that

∂ Q MCR = −2Ht y + 2(Ht H + μ2 I)x. ∂x

(5)

xˆ = (Ht H + μ2 I)−1 Ht y,

(6)

Hence

where I is a unitary matrix composed of values 1 in its main diagonal. 2.2. SPIHT SPIHT is a wavelet-based method developed initially for image and video compression [15]; it has been also evaluated to compress signals [16] including ECGs [9]. The SPIHT algorithm is one of the most efficient algorithms for compression. It belongs to the generation of wavelet encoders, which employs more sophisticated encoding. After the wavelet transform, SPIHT algorithm is used to encode the wavelet coefficients. The SPIHT algorithm orders the wavelet coefficients by magnitude and transmits them from the most significant to the least significant bit planes. To order the coefficients it uses SPIHT, which is designed on the basis of the self similarity. The algorithm does not sort all the coefficients by magnitude, but groups them according to successive thresholds. When a threshold value is given, it partitions the coefficients or the sets of coefficients into significant or insignificant coefficients. Whenever the algorithm determines the significance of a coefficient it produces one bit for the information. This algorithm has received widespread recognition for its notable success in various data compression field. As it has been said before, we apply in this work the SPIHT algorithm to encode the impulsional signal obtained from the deconvolution of the ECG signal. 3. Proposed algorithm The proposed algorithm requires several phases as described by the flowchart depicted in Fig. 1. In the first step, the baseline is removed from the recorded ECG signal. The obtained signal denoted y (seen as the output of a linear system

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Fig. 1. Flowchart describing the encoding and decoding phases.

as described by Eq. (2) is then deconvoluted using any normal PQRST ECG beat h, considered here as an impulse response. This beat is extracted easily from the signal to be processed and allows the construction of the Toeplitz matrix H. After the deconvolution process is achieved, the input signal denoted x having an impulsional aspect is estimated explicitly by Eq. (5). Each peak of this signal is detected and a set of N samples surrounding and including the peak are kept whereas the regions (segments) with low energy should be thresholded (threshold denoted ε ). The regions with energy lower than ε are transformed to zero-value segments. The threshold parameter ε is chosen in a way to be lower than the energy obtained from the main region. These zero-value segments are removed (to obtain an impulsional signal x˜ ) and should not be stored or transmitted. In fact, only their positions as well as the length (number of zero-value samples) are needed and kept into a specific frame denoted F. It should be used for the reconstruction process. Consequently, the encoding process achieves the following steps: 1. Transmission/storing x˜ after SPIHT coding. 2. Transmission/storing h after SPIHT coding. 3. Lossless encoding of F. To reconstruct the signal at the reception, zero-value segments (after decoding F) are integrated in SPIHT decoded signal x˜ . Finally, the obtained signal is then convoluted to h.

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Table 1 Statistical evaluation of the proposed scheme CR = 36

ECG signal

101 103 116 117 119

CR = 41

CR = 48

CR = 56

SPIHT

DPM-ECPI

SPIHT

DPM-ECPI

SPIHT

DPM-ECPI

SPIHT

DPM-ECPI

29.97 31.82 30.72 28.88 33.38

48.20 46.47 51.89 25.32 42.01

34.22 42.72 39.19 37.81 44.45

51.17 47.45 54.04 32.84 51.52

50.22 56.72 49.25 62.11 70.48

55.14 54.45 63.08 33.22 55.37

64.22 70.77 69.14 80.44 85.87

58.12 64.45 65.18 63.84 71.53

Note. The mean PRD are given for multiple CR values. SPIHT: direct encoding. DPM-ECPI: encoding using the deconvolution.

4. Results and discussion The DPM-ECPI has been evaluated on real signals from the well known MIT-BIH arrhythmia database. Each record in the database is acquired at a sampling rate of 360 samples/s and represented with a resolution of 11 bits. The processing is performed segment by segment. The length of each segment is 2048 samples. The impulse response h used in the deconvolution and the convolution technique is a typical ECG beat. Therefore, for minimum distortion, this beat is encoded using SPIHT at 0.5 bit/sample. At this rate, one can preserve the waves PQRST. Furthermore, the position of zero-value segments and their corresponding number of samples are encoded into the frame F using 11 bits. In fact, the number of bits is limited by the zero-value segment length (2048). 4.1. Regularization parameter μ Since the deconvolution is an ill-problem; choosing properly the regularization parameter μ is essential. Fortunately, this aspect has been widely discussed in the literature for both signal and image processing. One can for example refer to [17]. In our case, the method was tested for several values for the regularization parameter μ and finally it was fixed to the value that provides better results. 4.2. The number of samples N selected around each impulse The set of samples selected around each peak in the impulsional signal are the samples required for the reconstruction purpose. As N increases, the quality of the reconstructed ECG signal improves. In the other hand, when N increases, the CR systematically decreases. Consequently, for a given quality determined by the percent root-mean-square difference (PRD) in %; an optimal value of N can be obtained by minimizing this criterion. The PRD is defined as follows:

  N  2  1 (x(n) − x(n)) × 100, PRD =  n= N 2 n=1 x (n) 

(7)

where x and x represent respectively, original and reconstructed signal. The PRD is an objective criterion but it cannot replace the visual quality or the clinical evaluation, generally achieved by the physicians. The compression ratio is defined by CR = N x / N x , where N x denotes the number of bits in the original signal and N x denotes the number of bits after encoding. By comparing our proposed algorithm to a direct encoding using SPIHT (applied directly to ECG signal without deconvolution), one can show that for higher compression ratios, our method gives lower value for PRD. Typical reconstructed waveforms of records 117 and 119, along with the original ones are illustrated respectively in Figs. 2 and 3. However, in the first example and for a very high CR = 56, one can notice that the technique using the DPM-ECPI outperform clearly SPIHT algorithm. Even if the corresponding PRD seems to be high, ECG beats are perfectly identified. Consequently, all the clinical features related to latencies and amplitudes are well preserved. Furthermore, at this rate of compression, the direct application of SPIHT distorts completely the ECG signal which makes it clinically unusable. The curve corresponding to the evolution of the PRD versus the CR shows (see Fig. 4) that for high CRs, the DPM-ECPCI gives better results than the direct encoding while For low CRs the direct method achieves better performances. In the second example, the ECG represents a mixture of normal beats and premature ventricular contraction (PVCs). However, at a compression ratio of 26, the reconstructed ECG signal obtained by the DPM-ECPI is clinically exploitable since all the main feature are preserved; whereas using the direct SPIHT coding, one can notice that the morphology of the beats has been transformed, namely the disappearing of some P waves as well as an important distortion of the PVC beat. Similarly, as in the previous example, the curve CR-PRD (Fig. 5) shows that the proposed technique using the DPM-ECPI outperforms clearly the direct coding for high CR. The evaluation of the proposed technique has also been achieved statistically by encoding a certain number of common ECG signals from MIT-BIH database. The results are gathered in Table 1 where the mean PRD is given for various CRs. As it

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Fig. 2. Record 117 from MIT/BIH. From the top to bottom: original signal, deconvoluted signal, reconstructed signal using DPM-ECPI (for CR = 56, PRD = 63.8427, μ = 0.01, N = 61, energy threshold ε = 1.5), and reconstructed ECG signal using direct encoding (CR = 56, PRD = 80.44).

Fig. 3. Record 119 from MIT/BIH (with PVC). From the top to bottom: original signal, deconvoluted signal, reconstructed signal using DPM-ECPI (CR = 26, PRD = 33.8976, μ = 0.01, N = 31, energy threshold ε = 1.5) and reconstructed ECG signal using direct encoding.

can be noticed, the DPM-ECPI is more appropriate for high CRs which make it more convenient for transmission in narrow bandwidth network. 5. Conclusions We have presented in this paper a deconvolution preprocessing module for ECG codec performance improvement. As it has been seen previously, the module consists in transforming the ECG signal to be compressed to an impulsional one which is encoded using SPIHT.

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Fig. 4. The PRD versus CR for the record 117. For higher CR values the DPM-ECPI improves the performances compared to the direct encoding.

Fig. 5. The PRD in function of CR for record 119 from MIT/BIH. For higher CR values the DPM-ECPI improves the performances compared to the direct encoding.

Mainly, just significant impulses are needed to be transmitted. For the whole transmission of the ECG signal, the impulsional response is transmitted only one time whereas; the peak-positions frame is transmitted for each processed segment (2048 samples in our case). We have seen also that the proposed technique can be particularly used for high CRs. When low CRs are required, classical codecs become more suitable. Therefore, one can imagine a system that commutated automatically between a simple codec and the proposed scheme. In addition, to improve the technique, one can use an adaptive impulse response depending to the processed ECG. Finally, the method is very suited for progressive transmissions and on-request transmissions. For instance, if a physician is not satisfied by the quality of the received signal, he can just select the segment to be improved which corresponds to a request for increasing the parameter N. Hence, just few samples having low amplitudes should be transmitted. This aspect has not been deeply explored yet, but we believe that the future codecs should take into account the progressevity of transmission as well as the transmission on-request.

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References [1] A. Naït-Ali, C. Cavaro-Menard, Compression des Images et des Signaux Médicaux, Hermes, France, 2007. [2] A. Naït-Ali, C. Cavaro-Menard, Compression of Biomedical Images and Signals, ISTE/Wiley, 2008. [3] S.M. Jalaleddine, C.G. Hutchens, R.D. Strattan, W.A. Coberly, ECG data compression techniques—A unified approach, IEEE Trans. Biomed. Eng. 37 (1990) 329–343. [4] J. Cox, F. Noelle, H. Fozzard, G. Oliver, AZTEC: A preprocessing program for real time ECG rhythm analysis, IEEE Trans. Biomed. Eng. BME-15 (1968) 128–129. [5] L. Batista, E.U.K. Melcher, L.C. Carvalho, Compression of ECG signals by optimized quantization of discrete cosine transform coefficients, Med. Eng. Phys. 23 (2001) 127–134. [6] S.-G. Miaou, H.-L. Yen, C.-L. Lin, Wavelet-based ECG compression using dynamic vector quantization with tree code vectors in single codebook, IEEE Trans. Biomed. Eng. 49 (2002) 671–680. [7] B.A. Rajoub, An efficient coding algorithm for the compression of ECG signals using the wavelet transform, IEEE Trans. Biomed. Eng. 49 (2002) 355–362. [8] M.L. Hilton, Wavelet and wavelet packet compression of electrocardiograms, IEEE Trans. Biomed. Eng. 44 (1997) 394–402. [9] Z. Lu, D.Y. Kim, W.A. Pearlman, Wavelet compression of ECG signals by the set partitioning in hierarchical trees algorithm, IEEE Trans. Biomed. Eng. 47 (2000) 849–856. [10] G. Nave, A. Cohen, ECG compression using long-term prediction, IEEE Trans. Biomed. Eng. 40 (1993) 877–885. [11] A. Ouamri, A. Naït-Ali, ECG compression method using Lorentzian functions model, Digital Signal Process. 17 (2007) 319–326. [12] A. Chatterjee, A. Naït-Ali, P. Siarry, An input-delay neural network based approach for piecewise ECG signal compression, IEEE Trans. Biomed. Eng. 52 (2005) 945–947. [13] J.J. Anaya, L.G. Ullate, C. Fritsch, A method for real time deconvolution, IEEE Trans. Instrum. Measur. 41 (3) (1992) 413–419. [14] T. Dhaene, L. Martend, D. De Zutter, Generalized iterative frequency domain deconvolution technique, IMTC Conference, May 1993, pp. 85–87. [15] A. Said, W. Pearlman, A new fast and efficient image codec based on set partitioning in hierarchical trees, IEEE Trans. Circuits Syst. Video Technol. 6 (1996) 243–250. [16] C. Vijayaa, J.S. Bhatb, Signal compression using discrete fractional Fourier transform and set partitioning in hierarchical tree, Signal Process. 86 (2006) 1976–1983. [17] N.P. Galatsanos, A.K. Katsaggelos, Methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation, IEEE Trans. Image Process. 1 (3) (1992) 322–336.

Lina El Khansa was born in 1980 in Ghobeiri (Lebanon). She received the B.S. degree in biomedical engineering in Lebanon, then the M.S. degree in biomedical engineering from the University Paris 12 in 2004. Currently, she is preparing the Ph.D. degree in biomedical engineering at the same university. Her research interests are focused on physiological signal processing. Amine Nait-Ali was born in 1972 in Oran (Algeria). He received the B.S. degree in electrical engineering from University of Sciences and Technology of Oran, then the DEA degree in automatic and signal processing from University Paris XI in 1995. He received the Ph.D. degree in biosignal processing in 1998 and finally the “Accreditation to Direct Research” (HDR) degree from University Paris XII in 2007. He is currently an Associate Professor at the same university. His research interests are focused on biosignal processing, optimization, modeling and medical signal and image compression. Mohamad Khalil was born in 1973 in Akkar Atika (Lebanon). He obtained an engineering degree in electrical and electricity from the Lebanese University, Faculty of Engineering, Tripoli, Lebanon, in 1995. He received the DEA degree in biomedical engineering from the University of Technology of Compiegne (UTC) in France in 1996. He received the Ph.D. degree from the University of Technology of Troyes in France in 1999. He received the HDR (Habilitation à Diriger des Recherches) degree from UTC in 2006. He is currently researcher at several universities in Lebanon including the Lebanese University. His current interests are the signal and image processing problems: detection, classification, analysis, representation and modeling of nonstationary signals, with application to biomedical signals and images.