On the use of PRD and CR parameters for ECG compression

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1 Medical Engineering & Physics 27 (2005) Communication On the use of PRD and CR parameters for ECG compression Manuel Blanco-Velasco a,, Fernando Cruz-Roldán a, J. Ignacio Godino-Llorente b, Joaquín Blanco-Velasco a, Carlos Armiens-Aparicio a, Francisco López-Ferreras a a Dep. Teoría de la Señal y Comunicaciones, Escuela Politécnica, Universidad de Alcalá, Alcalá de Henares (Madrid), Spain b Dep. Ingeniería de Circuitos y Sistemas, Universidad Politécnica de Madrid, Madrid, Spain Received 4 August 2004; received in revised form 21 January 2005; accepted 22 February 2005 Abstract The quality measurement of the reconstructed signal in an electrocardiogram (ECG) compression scheme must be obtained by objective means being the percentage root-mean-square difference (PRD) the most widely used. However, this parameter is dependent on the dc level so that confusion can be stated in the evaluation of ECG compressors. In this communication, it will be shown that if the performance of an ECG coder is evaluated only in terms of quality, considering exclusively the PRD parameter, incorrect conclusions can be inferred. The objective of this work is to propose the joint use of several parameters, as simulations will show, effectiveness and performance of the ECG coder are evaluated with more precision, and the way of inferring conclusions from the obtained results is more reliable IPEM. Published by Elsevier Ltd. All rights reserved. Keywords: Electrocardiogram (ECG); Wavelet packets (WP); Filter bank 1. Introduction The use of wavelet in electrocardiogram (ECG) analysis was first proposed in [1]. From that moment, a wide variety of ECG wavelet-based compressors have been developed whose main goal is to improve the compression ratio (CR). As examples, [2,3] are compression schemes carried out by means of discrete wavelet transform (DWT), whereas [4,5] are wavelet packets-based algorithms. Recently, a technique based on vector quantization has demonstrated good performance obtaining a very high CR but suffering from high computational complexity [6]. On the other side, several algorithms have also been developed using efficient and very easy techniques based on thresholding (see references [7 10]). The above algorithms work with sufficient speed to be implemented in real time and provide good compression ratios. However, when using the percentage root-mean-square difference (PRD) formula care must be taken. Moreover, as Corresponding author. Tel.: ; fax: address: manuel.blanco@uah.es (M. Blanco-Velasco). there are several differences in the way of showing the results, conclusions have to be extracted under similar conditions. In this communication, we explain our view of the way of inferring conclusions from the behaviour and performance of the algorithms developed. We analyse the influence of the dc level added to ECG signals on the coder performance. Simulations of different compression algorithms under similar conditions show that final conclusions strongly depend on the parameter chosen for evaluating the quality. For this reason, we propose the joint use of more than one parameter. 2. The PRD expression 2.1. Performance measurement Let x[n] and ˆx[n] be the original and the reconstructed signals, respectively, and N its length. The PRD formula is defined as: Nn=1 (x[n] ˆx[n]) PRD = 2 Nn= (1) (x[n]) /$ see front matter 2005 IPEM. Published by Elsevier Ltd. All rights reserved. doi: /j.medengphy

2 This parameter as quality measurement can mask the real performance of an algorithm since the PRD depends a lot on the mean value of the original signal. Zigel et al. clearly established in the Results and Discussion section of [11] that when using the PRD care must be taken to remove the baseline, or at least, to eliminate the dc level. To avoid this problem, several authors suggest the well-known definition for the PRD independent of the mean value, which is Nn=1 (x[n] ˆx[n]) PRD1 = 2 M. Blanco-Velasco et al. / Medical Engineering & Physics 27 (2005) Nn=1 100, (2) (x[n] x[n]) 2 where x[n] is the mean value of the signal x[n]. This is very important when the MIT-BIH arrhythmia database is used to carry out tests, as a baseline of 1024 is added to each database signal for storage purposes. Even if the baseline is removed, the dc level is never zero. The algorithm proposed in a previous work [9] was compared with both the set partitioning in hierarchical trees (SPIHT) [8] and the analysis by synthesis ECG compressor (ASEC) [12] using the same set of signals from the MIT-BIH arrhythmia database. To be precise, two database sets were selected: The first database proposed in [8] uses 10-min long data from records 1 : 100, 101, 102, 103, 107, 109, 111, 115, 117, 118 and 119. The second database proposed in [12] uses 1-min long data from records: 104, 107, 111, 112, 115, 116, 118, 119, 201, 207, 208, 209, 212, 213, 214, 228, 231 and 232. The performance of each of the three cases was measured in the following way: In [9], the original signal is mean removed and normalized to guarantee that all significant coefficients of a transform are scaled to values less than one. After decompression, the mean is added and formula (1) is applied, in this way the PRD is calculated from the ECGs with the 1024 baseline included. In [8], the 1024 baseline is removed by subtracting 1024 from each data sample, but the mean value of each ECG remains. In [12], PRD1 formula (2) is used, so the results will be the same whatever the mean value of the signals is. As we can see, the quality of the reconstructed signal can be correctly calculated by using Eq. (2). In this way, we have developed both the algorithm proposed in [9,8] (the arithmetic coder for the SPIHT algorithm was not included). The results from ASEC in [12] will remain unchanged. We have applied the same two sets of data, and carried out the tests in two different ways: Fig. 1. Performance measurements for compressing two ECG data sets using different ECG coders. The PRD formula is applied as explained in [8,9,12]. (1) As explained in [9,8]; the results are depicted in [9] (Fig. 4), and reproduced in Fig. 1. (2) With formula (2) to ensure the independence of the results from the mean value. The corresponding results are depicted in Fig. 2. Fig. 2 shows a performance comparison of the different ECG coders using the same parameter of measure. We can see that as far as the PRD is concerned, the performance of the algorithm in [12] is better than the algorithms proposed in [9,8]. Recently, a new distortion measure called weighted diagnostic distortion (WDD) has been developed [11] specifically for ECG compression. It is based on PQRST diagnostic features and it has been demonstrated very well correlated with cardiologists perception. Despite this advantage, the scientific community does not use it because of its high 1 We refer to the data from the MIT-BIH arrhythmia database as records taking into the account that each number represents a file that holds two ECGs. At no time is it specified by any of the authors of the references, which of the two channels are used to carry out the tests. In our case, both ECGs of each file or record have been used to do the tests. Fig. 2. Performance measurements for the compression of two sets of ECG data using different ECG coders. In this case, the PRD1 formula is used.

3 800 M. Blanco-Velasco et al. / Medical Engineering & Physics 27 (2005) complexity in calculation. Therefore, the PRD remains as the most widely used quality criterion. Besides the problems explained before, the PRD is a global criterion that does not take into account local effects. Nevertheless, they are often very significant in medical diagnosis based on signals, so it worth to complement with other quality measures. For instance, the measure of the maximum differences could contribute to give an idea about local effects. This can be achieved by means of the maximum amplitude error (MAX) measurement [13]: MAX = max{ x[n] ˆx[n] }. (3) n Another way could be the visual study of error signal e[n] calculated as e[n] = x[n] ˆx[n]. (4) 2.2. Pre-processing Several authors propose a pre-processing in which the original signal is mean removed and normalized to guarantee that all the significant coefficients of a transform remain scaled to values less than one. Care must be taken as this assertion can not always be guaranteed. For example, working with the MIT-BIH Arrhythmia Database and the preprocessing technique proposed in [9], we have found at least three records, 107, 119 and 118 where several wavelet coefficients are greater than one. Fig. 3 shows record 119 where only one coefficient is greater than one. Although it may seem that one coefficient would not contribute very much to the quality of the signal, we can see in Fig. 4 just how much it does affect the reconstructed signal. Here we can see the original signal (record 119) as a continuous line and the reconstructed signal as a broken line, both superimposed. At the top, the retrieved signal was obtained using the compression algorithm Fig. 4. Effect of pre-processing proposed in [9] on record 199. Table 1 Quality of signals represented in Fig. 3 Graphics from Fig 3 PRD PRD1 Top Bottom proposed in [9], and the corresponding pre-processing. The reconstructed QRS complex does not exactly match the original. To compensate, we have modified the pre-processing algorithm in the following way, so that all the wavelet coefficients remain less than one. As shown at the bottom of Fig. 3, the QRS complex can be reasonably well reconstructed using the same compression algorithm and modifying the pre-processing. Table 1 shows that the quality improvement almost doubles when all the wavelet coefficients are considered. 3. Analysing experimental results with the CR expression Fig. 3. First 2048 samples of record 119 and its wavelet coefficients. The aim in ECG compression is to increase the compression ratio (CR) but not at the expense of the quality of the reconstructed signal. The same can be stated in the other sense, i.e, any quality improvement can not be achieved at the expense of CR. Therefore, to infer conclusions from experimental results, the quality must always be analysed together with other compression parameter, for example, the compression ratio (CR). Table 2 shows an extract of results presented in [14] where the thresholding-based algorithm proposed in [9] was implemented using 1-min data from file 117 of the MIT-BIH arrhythmia database. Thresholding of the wavelet coefficients is done based on a desired energy packing efficiency (EPE)

4 M. Blanco-Velasco et al. / Medical Engineering & Physics 27 (2005) Table 2 Results extracted from those presented in [14] EPE A5 = CR CR PRD1 PRD1 7 bits 10 bits 7 bits 10 bits EPE D5 = and EPE D4 1 = EPE D5 = 0.97 and EPE D4 1 = EPE D5 = 0.97 and EPE D4 1 = EPE D5 = 0.97 and EPE D4 1 = Table 3 Maximum CR calculated for the first 2048 samples of record 117 EPE A5 = N x H N s N v CR max EPE D5 = 0.97 and EPE D4 1 = EPE D5 = 0.97 and EPE D4 1 = [9]. Then, the significance map is run-length encoded and the significant coefficients are quantized with 7 and 10 bits per sample respectively. In [14], the authors assert that using 10 bits to represent the significant coefficients improves the quality of the retrieved signal (both PRD1 and signal to noise ratio (SNR)), which is obvious as the quantization error decreases as more bits are used. If there is an improvement in the PRD1, we can only conclude that the performance of the algorithm has improved either if the CR remains constant or if it enhances as well, but this is not the case. Table 2 outlines the results reported in [14] showing the decrease in both the CR ( CR) and the PRD1 ( PRD1), which means worse compression ratio and better quality. If we take the second row, (EPE D5 = 0.97 and EPE D4-1 = 0.95), as a representative case, we can see that although the PRD1 improves by 1.03%, the CR decreases by 4.6 becoming worse. The fourth row shows how the PRD1 hardly varies though the CR decreases dramatically. With these results, it would be better to point out that it does not worth to encode the significant coefficients with more than 7 bits as the PRD1 improves only a few at the expense of the CR. Thresholding-based of wavelet coefficients algorithm come to be efficient from both the CR and implementation cost point of view. However, the direct implementation of the algorithm over a large amount of data cannot be applied in real-time due to the huge time requirements and the huge memory needs. This is the case of [14] where the algorithm is carried out with a 10-min long signal. This can be resolved by segmenting the incoming signal but at the expense of CR. In order to give an idea of how the performance of an algorithm can change, we have worked with the technique developed in [14] whose results are reported in Table 2. Since the compression technique is thresholding-based, a reasonable segment length of say 2048 samples would make the significant map long enough to be compressed adequately and the memory requirements would not increase too much. Record 117 was used under these conditions to make tests. The compression ratio is defined as CR = N x H + N s + N v. (5) An outline of our results is shown in Table 3. N x denotes the number of bits of the original signal, which as the precision of MIT-BIH arrhythmia database records is 11, is H is the header information. For a 2048-segment length, 46 bits can be used. The first 11 to store the total number of wavelet coefficients, the next 11 to store the index value of the last significant coefficient, the next 12 bits for the maximum magnitude of the original signal and the last 12 bits to store the mean of the normalized signal. N s denotes the number of bits used to code the significant coefficients, which in this case, as shown in the corresponding column of Table 3, N s is calculated as the number of significant coefficients multiplied by the numbers of bits used to represent each coefficient, which is 7. Finally, N v is the number of bits in the compressed significant map. To obtain the value of N v, we must determine the number of streams of consecutive 0 or 1 in the significant map. Based on the coding scheme, the minimum number of bits needed to code each stream is 6 (see [9] for more details). In this way, the resulting CR is the maximum for the first segment. The values for both examples are shown in Table 3.For the following segments, the performance is almost the same. As we can see, those values are substantially less than those obtained without segmenting (shown in Table 2). 4. Conclusions In this communication, we propose the joint use of several parameters in order to evaluate the effectiveness and performance of an ECG coder. Both PRD and CR have been chosen because they are the parameters most commonly used by the international community. The aim in ECG compression is to increase the compression ratio (CR) but not at the expense of the quality of the reconstructed signal. The same can be stated in the other sense, i.e, any improvement in the quality can not be done at the expense of CR. We analysed the influence of the baseline added to the MIT-BIH Arrythmia Database signals on the ECG coders performance. Our results confirm that the way of inferring conclusions from the obtained results, considering only the PRD and the CR parameters independently, can hide the real performance of

5 802 M. Blanco-Velasco et al. / Medical Engineering & Physics 27 (2005) the compressor. In the process of designing a new ECG coder, it is interesting to use jointly several parameters related to the compression ratio as well as the measure of the distortion in order to achieve a thorough analysis. Therefore, we propose that, the quality must always be analysed together with different parameters (for example, a joint use of PRD1 and CR). Moreover, conditions of simulations should be explained with the details necessary to allow the reader judging the results. Acknowledgment The authors would like to thank the anonymous reviewers for their helpful suggestions, which have considerably improved the quality of this paper. This work was supported in part by grants PI2004/005, PI2005/066, and PI2005/074 from University of Alcalá. References [1] Senhadji L, Bellanger JJ, Garrault G, Coatrieux JL. Wavelet analysis of ECG signals. Proceedings of the 12th Annual International on Conference of the IEEE Engineering in Medicine and Biology, vol pp [2] Chen J, Itoh S, Hashimoto T. ECG data compression by using wavelet transform. IEICE Transactions on Information and Systems December 1993;E76D(12): [3] Djohan A, Nguyen TQ, Tompkins WJ. ECG compression using discrete symmetric wavelet transform. Proceedings of the 17th Annual International on Conference of the IEEE Engineering in Medicine and Biology, vol pp [4] Hall J, Crowe J. Ambulatory electrocardiogram compression using wavelet packets to approximate the Karhunen Loeve transform. Applied Signal Processing 1996;3: [5] Bradie B. Wavelet packets-based compression of single lead ECG. IEEE Transactions on Biomedical Engineering May 1996;43(5): [6] Miaou S-G, Yen H-L, Lin C-L. Wavelet-based ECG compression using dynamic vector quantization with tree codevectors in single codebook. IEEE Transactions on Biomedical Engineering July 2002;49(7): [7] Hilton ML. Wavelet and wavelet packets compression of electrocardiogram. IEEE Transactions on Biomedical Engineering May 1997;44(5): [8] Lu Z, Kim DY, Pearlman WA. Wavelet compression of ECG signals by the set partitioning in hierarchical trees algorithm. IEEE Transactions on Biomedical Engineering July 2000;47(7): [9] Rajoub BA. An efficient coding algorithm for the compression of ECG signals using the wavelet transform. IEEE Transactions on Biomedical Engineering April 2002;49(4): [10] Abo-Zahhad M, Rajoub BA. An effective coding technique for the compression of one-dimesional signals using wavelet transforms. Medical Engineering and Physics April 2002;24(3): [11] Zigel Y, Cohen A, Katz A. The weighted diagnostic distortion (WDD) measure for ECG signal compression. IEEE Transactions on Biomedical Engineering November 2000;47(11): [12] Zigel Y, Cohen A, Katz A. ECG signal compression using analysis by synthesis coding. IEEE Transactions on Biomedical Engineering October 2000;47(10): [13] Blanco-Velasco M, Cruz-Roldán F, López-Ferreras F, Bravo-Santos Á, Martínez-Munóz D. A low computational complexity algorithm for ECG signal compression. Medical Engineering and Physics September 2004;26(7): [14] Alshamali A, Al-Fahoum AS. Comments on An efficient coding algorithm for the compression of ECG signals using the wavelet transform. IEEE Transactions on Biomedical Engineering August 2003;50(8):