The Weighted Diagnostic Distortion (WDD) Measure for ECG Signal Compression

Transcription

1 1422 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL 47, NO 11, NOVEMBER 2000 The Weighted Diagnostic Distortion (WDD) Measure for ECG Signal Compression Yaniv Zigel*, Arnon Cohen, and Amos Katz Abstract In this paper, a new distortion measure for electrocardiogram (ECG) signal compression, called weighted diagnostic distortion (WDD) is introduced The WDD measure is designed for comparing the distortion between original ECG signal and reconstructed ECG signal (after compression) The WDD is based on PQRST complex diagnostic features (such as P wave duration, QT interval, T shape, ST elevation) of the original ECG signal and the reconstructed one Unlike other conventional distortion measures [eg percentage root mean square (rms) difference, or PRD], the WDD contains direct diagnostic information and thus is more meaningful and useful Four compression algorithms were implemented (AZTEC, SAPA2, LTP, ASEC) in order to evaluate the WDD A mean opinion score (MOS) test was applied to test the quality of the reconstructed signals and to compare the quality measure (MOS error ) with the proposed WDD measure and the popular PRD measure The evaluators in the MOS test were three independent expert cardiologists, who studied the reconstructed ECG signals in a blind and a semiblind tests The correlation between the proposed WDD measure and the MOS test measure (MOS error ) was found superior to the correlation between the popular PRD measure and the MOS error Index Terms Electrocardiogram, ECG compression, distortion measures, PRD, PQRST complex, weighted diagnostic distortion preserve the relevant diagnostic information The main problem here is that such information is subjective and is determined by the expert cardiologists perception The problem has been defined in the past as diagnostability [18] The problem of objective evaluation criteria arises in many applications where the resultant processed signal is to be presented to a human operator, such as in the case of speech and image processing [19] Today the accepted way to examine diagnostability is to get cardiologists evaluations of the system s performance This solution is expensive and may be applied only for research or offline evaluation of coder s performance Its advantage, of course, lies in the fact that it yields direct information on experts impression As yet, there is no mathematical measure which is correlated with diagnostic information Such a measure is described in this paper It has been successfully used in an ECG compression system [20], [31] II CONVENTIONAL DISTORTION MEASURES In most ECG compression algorithms, the PRD measure is employed I INTRODUCTION MANY algorithms for electrocardiogram (ECG) compression have been proposed in the last 30 years [1] [17] Until recently, all ECG compression algorithms have used simple mathematical distortion measures such as the percentage root mean square (rms) difference (PRD) for evaluating the reconstructed signal Such measures are almost irrelevant from the point of view of diagnosis In this paper, a new distortion measure for ECG signal compression called weighted diagnostic distortion (WDD), based on diagnostic features is introduced One of the important problems in ECG compression is the definition of the error criterion The purpose of the compression system is to remove redundancy, the irrelevant information (which does not contain diagnostic information in the ECG case) Consequently, the error criterion has to be defined such that it will measure the ability of the reconstructed signal to where is the original signal, is the reconstructed signal, and is the length of the window over which the PRD is calculated Some papers use a version of PRD with different normalization where is the signal s mean Definition (2) is independent of the dc level of the original signal Definitions (1) and (2) are of course the same, for a signal with zero mean In the literature, there are some other error measures for comparing original and reconstructed ECG signals [21], such as the root mean square error (rms): (1) (2) Manuscript received October 27, 1999; revised June 30, 2000 Asterisk indicates corresponding author *Y Zigel is with the Electrical and Computer Engineering Department, Ben-Gurion University, PO Box 653, Beer-Sheva 84105, Israel ( yaniv@eebguacil) A Cohen is with the Electrical and Computer Engineering Department, Ben- Gurion University, Beer-Sheva 84105, Israel A Katz is with the Cardiology Department Faculty of Health Sciences, Ben- Gurion University, Beer-Sheva 84105, Israel Publisher Item Identifier S (00) or the signal-to-noise ratio (SNR), which is expressed as (3) (4) /00$ IEEE

2 ZIGEL et al: THE WDD MEASURE FOR ECG SIGNAL COMPRESSION 1423 The relation between the SNR and the PRD (2) is: A maximum amplitude error [21], or peak error (MAX or PE), is also an error measure, which may be used in ECG compression; it is expressed as (5) All these error measures have many disadvantages, which all result in poor diagnostic relevance For example, if the signal has baseline fluctuations, the variance of the signal will be higher, the PRD will be artificially lower, and the SNR will be artificially higher Furthermore, every segment in the PQRST complex has a different diagnostic meaning and significance A given distortion in one segment does not necessarily have the same weight as the same distortion in another segment For example, in many patients ECGs, the ST segment is much more diagnostically significant than the TP segment Fig 1 Some of the amplitude and duration diagnostic features III THE WDD MEASURE The proposed WDD measure was first introduced in [22] This measure is based on comparing the PQRST complex features of the two ECG signals, the original ECG signal and the reconstructed one (the signal recovered from the compressed signal) The WDD measures the relative preservation of the diagnostic information in the reconstructed signal The relevant diagnostic information in the ECG signals exists in the form of PQRST complex features The PQRST complex features (diagnostic features) are the location, duration, amplitudes, and shapes of the waves and complexes that exist in every beat (PQRST complex) These were chosen with the help of an experienced cardiologist A The Diagnostic Features The diagnostic features can be divided into three groups: duration features (of waves, segments, and intervals), amplitude features, and shape features The duration features are the most significant features in most of the applications Fig 1 shows some amplitude and duration of the diagnostic features The WDD requires the extraction of the location, the amplitudes and the shapes of the PQRST waves and segments B Diagnostic Feature Extraction The main effort in the PQRST feature extraction is the segmentation, namely the determination of the exact location of the waves (Fig 2 shows an example of PQRST waves and the location points) After segmentation, the determination of the waves amplitudes and shapes is much simpler The strategy for finding the waves locations is to first recognize the QRS complex, which has the highest frequency components The T wave is recognized next, and, finally, the P wave, which is usually the smallest wave The baseline and the ST features are relatively easily estimated later [22], [29] Several algorithms for ECG segmentation have been suggested Most are based on time and frequency domain recognition of the waves [23] [26], but other methods such as for example HMM segmentation [27] have also been published Fig 2 PQRST waves and location points of one beat C The WDD Measure For every beat of the original signal and for the reconstructed signal, a vector of diagnostic features is defined original signal (6) reconstructed signal (7) where is the number of features in the vector, is used in this work The diagnostic parameters were chosen to be: Table I describes these features The WDD between these two vectors is where is the normalized difference vector and and is a diagonal matrix of weights, defined in (16) below Every scalar in this vector gives the distance between the original signal feature and the reconstructed signal feature For the (8) (9)

3 1424 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL 47, NO 11, NOVEMBER 2000 TABLE I DESCRIPTION OF THE DIAGNOSTIC FEATURES ( 10 mm = 1 mv) duration features and the amplitude features, the distance is defined as The values of the matrices that were used in this work were (10) For the shape features (, and ), the distance is determined by fixed penalty matrices (one matrix for each shape feature) (13) (14) (11) where is the number of shapes for the relevant feature ( for for, and for ) Each element of the penalty matrices is the cost measure or the distance between the shape code and the shape code of the original shape feature and the reconstructed one, respectively is determined such that its value is between 0 to 1, for, and For the shape features, the distance is given as: Table II describes the shape features and their codes (12) (15) where the shapes are numbered as Table II shows The types of shapes were determined using an experienced cardiologist, and the penalty matrices were determined arbitrarily using the subjective logic of noncardiologist The algorithm for the estimation of shape features may be found in [29]

4 ZIGEL et al: THE WDD MEASURE FOR ECG SIGNAL COMPRESSION 1425 TABLE II THE CODING OF THE WDD SHAPE FEATURES [in (8)] is a diagonal weighting matrix (16) TABLE III THE BLIND MOS TEST QUESTIONNAIRE This matrix provides a way to emphasize certain parameters or regions in the ECG complex When compressing the ECG of a certain subject, the matrix may be adjusted to match the effects of the specific pathology (for example emphasizing the ST segment) Note that in (8) the WDD is normalized to the sum of the weights The values of the weights: which were determined for checking the algorithm, are determined to be as shown in (17) at the bottom of the page For the sake of this work, the weights were determined arbitrarily using the subjective logic of a noncardiologist In practice, the weights should reflect the relevant clinical importance of the features The extraction of the diagnostic features used for the WDD is described in [29] Some other feature extraction algorithms may be used Of course, lack of precision in the extraction is a source of error and can affect the WDD score of a reconstructed signal IV THE MEAN OPINION SCORE (MOS) TEST In order to analyze the proposed WDD measure, a reference qualitatively based distortion measure is needed, which represents the true quality of every reconstructed signal ( gold standard) Therefore, MOS test was performed, which contained a blind test and a semiblind test (these two tests, in medical terms, are single-blind tests, because the tested signals are known to the test manager but not to the test evaluators the cardiologists) The evaluators for this test were three experienced cardiologists The results of this MOS test are combined in a distortion measure, called: Every tested signal (reconstructed ECG signal), was printed on paper, in the form and the scale that a cardiologist is used to seeing The aim of the blind-test was to get the cardiologists evaluation of reconstructed signals from different compression algo- rithms without knowing the source of each tested signal (original, reconstructed and the compression method) In every test, the cardiologist was given one strip of signal (marked by a serial number), which contained the unknown signal and some mean estimated features (see example in Fig 3) The signal was one channel, 27 seconds in duration [29] For every tested signal, the cardiologist was asked to fill a questionnaire, which is shown in Table III The aim of the semiblind test was to get cardiologists evaluation of reconstructed signals from different compression algorithms by comparing each of the reconstructed signals (without knowing the compression method) to the original signal In every test, the cardiologist was given one strip of signal, which contained the original signal (marked as original ) and the reconstructed signal (marked as reconstructed ) 135 seconds were allocated for each signal (see example in (17)

5 1426 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL 47, NO 11, NOVEMBER 2000 Fig 4 One of the strips used for the semiblind test Fig 3 One of the strips used for the blind test Each line is the continuation of the previous line (total duration is 27 seconds) The vertical grid lines are 02 second (5 mm) apart The horizontal grid lines are 05 mv (5 mm) apart The feature values on the bottom are the mean values TABLE IV THE SEMI-BLIND MOS TEST QUESTIONNAIRE Fig 4) The evaluator was aware of which strip is original and which is reconstructed, however he was not aware of the compression algorithm and its parameters For every tested signal, the cardiologist was asked to fill a questionnaire, which is shown in Table IV A weighted MOS error was calculated from the results of the blind and semiblind tests of three independent cardiologists for every tested signal For the blind test, the MOS error of one tested signal is the relative error (in percentage) between the evaluation of the reconstructed signal and the evaluation of the suitable original signal The MOS error of one tested signal from the th cardiologist is given by factor factor (18) where general quality score of the reconstructed signal (1 5); general quality score of the original signal (1 5); interpretation of the th parameter of the reconstructed signal (1 8);

6 ZIGEL et al: THE WDD MEASURE FOR ECG SIGNAL COMPRESSION 1427 interpretation of the th parameter of the original signal (1 8); factor weighting coefficient between the general quality score and the interpretation (in the experiments performed here: factor ); number of the testing cardiologist The MOS error for the blind-test of one tested signal from all cardiologists was then calculated by (19) For the semiblind test, the MOS error (by percentage) of one tested signal from the cardiologist is given by: factor factor (20) where factor measure of similarity between the original signal and the reconstructed one (1 5); answer to the Boolean question about the diagnosis (0 YES, 1 NO); weighting coefficient between the measure of similarity and the Boolean question factor For the semiblind test, the MOS error of one tested signal from all cardiologists is given by The MOS error of one tested signal is given by (21) (22) The lower the value of the the better the quality evaluation of the reconstructed signal This is perhaps different from other applications (such as the speech MOS test), where the higher the value of the MOS the better the signal quality The in this work was defined as such in order to be similar to the PRD/WDD measures V RESULTS AND DISCUSSION Four compression algorithms were implemented in order to yield reconstructed signals with different qualities The reconstructed signals were used for analysis and comparison between the WDD and the PRD measure The ECG signals were taken from the MIT-BIH Arrhythmia database [30] and the compression algorithms were chosen to be: analysis by synthesis ECG compressor (ASEC) with WDD minimization and with PRD minimization [20], [31], LTP [13], SAPA2 [8], and AZTEC [3] These compressors were chosen, because AZTEC and SAPA2 are often referred for comparison in the literature, and ASEC and LTP are two of the best ECG compressors available today ECG records from the MIT-BIH database (records: 104, 107, 111, 112, 115, 116, 118, 119, 201, 207, 208, 209, 212, 213, 214, 228, 231, and 232) were used in the evaluation These signals were chosen by an experienced cardiologist and they consist of a large variety of pathological cases Every original signal was Fig 5 The scattering of the distortion measures for the reconstructed signals (the sloping lines are the regression lines and the dashed rectangles are the quality areas of reconstructed signals (a) The scattering of PRD versus MOS, (b) The scattering of WDD versus MOS preprocessed to have zero mean and flat baseline From these 18 original signals, 92 reconstructed records were produced For every reconstructed signal, three distortion measures were calculated: WDD, PRD, and (from the MOS test described before) The was used as the gold standard Fig 5 shows the scattering of the distortion measures for the reconstructed signals Each point represents the distortion values of one reconstructed record Fig 5(a) shows the scattering of PRD versus, and Fig 5(b) shows the scattering of WDD versus The results were analyzed in two ways: 1) A measure of deviation from the regression line between two distortion measures was defined It is given as the variance of the points vertical deviation from the regression line where (23) vertical deviation of the th point from the regression line; total number of points (signals); mean value of

7 1428 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL 47, NO 11, NOVEMBER 2000 TABLE V QUALITY GROUPS DEFINED BY MOS The regression line (the linear lines in Fig 5) and the variance were calculated with the MATLAB function regressm, which was programmed using equations from [32] The deviation variance between the PRD and the MOS error [Fig 5(a)] is 8091, and the deviation variance between the WDD and the MOS error [Fig 5(b)] is 2204, four times better than the PRD case 2) A rough classification of signal quality was defined by dividing the into four quality groups [33] These are shown in Table V The ability of the distortion measure (PRD or WDD) to predict the quality of the ECG record was then examined For every tested measure (PRD and WDD), four prediction ranges were determined Fig 6 shows the PRD and WDD values of each quality group of signals and these ranges The boundaries (thresholds) of each prediction range were manually determined, such that all the signals in the prediction range (except 3% outliers) would be included in a minimum number of quality groups For example, in the PRD was determined to be 2 For this value, all the signals in the first prediction range (PRD: 0 2) belong to the very good quality group in the same case was determined to be 9, because for this value, all the signals in the second prediction range (PRD: 2 9) belong to the very good and good quality groups the minimum number of quality groups Table VI shows the prediction ranges of the tested measures and their quality group connection (confusion matrix) Every number inside the 4 4 matrix, is the percentage of signals from the th prediction range, which belong to the th quality group (including outliers) Table VI demonstrates the prediction ability of the two distortion measures For example, if some signal has a PRD between 9% 19%, one can not determine its quality group, while the range of WDD between predicts a quality group of good or not good The percentage numbers on the main diagonal represent the correct prediction The mean correct prediction of the WDD is 59% while that of the PRD is only 405% Furthermore, let us define normalized prediction error as follows: (24) where is the weight of the th row and the th column, defined as follows: (25) The normalized prediction error of the WDD is 1025% while that of the PRD is 204% The superiority of the WDD over the PRD is clearly demonstrated by these results Fig 6 The scattering and thresholds of the prediction ranges for each quality group of reconstructed signals (outliers are marked with x) (a) For the PRD measure, (b) for the WDD measure TABLE VI MEASURES RANGES AND QUALITIES CONNECTION Fig 7 shows an example of original ECG signal (from MIT-BIH record 214) and two extremely bad quality reconstructed signals Observing these signals and the values, one can say that these reconstructed signals are definitely bad quality signals Fig 8 shows an example of two very good quality reconstructed signals Observing these signals and the values, one can say that these reconstructed signals are very good quality signals Note that the PRD value for the bad SAPA2 reconstructed signal [Fig 7(c)] is 92%, which is less than the PRD value (1541%) for the very good ASEC reconstructed signal

8 ZIGEL et al: THE WDD MEASURE FOR ECG SIGNAL COMPRESSION 1429 The ASEC consists of WDD minimization, and it is superior to most available compression algorithms A detailed information and results of this compression algorithm can be found in [20], [29], and [31] The PRD measure has the advantage of low complexity It is very inexpensive to calculate the PRD We emphasize again that when using the PRD, care must be taken to remove the baseline (to have zero and flat baseline), or, at least, to eliminate the dc component of the signal The WDD measure is well correlated with cardiologists perception Its disadvantage is the fact that it is expensive to calculate In cases where the automatic diagnostic features are required for other purposes than compression (screening, monitoring, alarms), this may not be a disadvantage The WDD may be calculated in real time by a digital signal coprocessor, or by a sufficiently powerful CPU Based on the results reported here, it is concluded that the proposed WDD measure is much more suitable for evaluating ECG reconstructed signals than the popular PRD measure REFERENCES Fig 7 Example of bad quality reconstructed signals (a) Original ECG signal (MIT-BIH record 214), (b) reconstructed signal, which was compressed by the AZTEC algorithm The distortion values for this signal are: MOS = 67:9%; PRD = 10:6%, and WDD = 30:1%, (c) reconstructed signal, which was compressed by the SAPA2 algorithm The distortion values for this signal are: MOS =71:2%; PRD = 9:2%, and WDD = 21% Fig 8 Example of very good quality reconstructed signals (a) Original ECG signal (MIT-BIH record 214), (b) reconstructed signal, which was compressed by the LTP algorithm The distortion values for this signal are: MOS = 12:1%; PRD = 7:88%, and WDD = 7:55% (note the addition of high frequency low amplitude noise), (c) reconstructed signal, which was compressed by the ASEC algorithm (with WDD minimization) The distortion values for this signal are: MOS = 3:33%; PRD = 15:41%, and WDD = 3:52% [Fig 8(c)] This is a clear example of the diagnostic irrelevance of the PRD measure [1] J P Abenstein and W J Tompkins, A new data reduction algorithm for real time ECG analysis, IEEE Trans Biomed Eng, vol BME-29, pp 43 48, Jan 1982 [2] G D Barlas and E S Skordalakis, A novel family of compression algorithms for ECG and other semiperiodical, one dimensional, biomedical signals, IEEE Trans Biomed Eng, vol 43, Aug 1996 [3] J R Cox, F M Nolle, H A Fozzard, and C G Oliver, AZTEC, a preprocessing program for real time ECG rhythm analysis, IEEE Trans Biomed Eng, vol 15, pp , Apr 1968 [4] B Furht and A Perez, An adaptive real-time ECG compression algorithm with variable threshold, IEEE Trans Biomed Eng, vol 35, pp , June 1988 [5] D J Hamilton, D C Thomson, and W A Sandham, ANN compression of morphologically similar ECG complexes, Med Biol Eng Comput, vol 33, pp , Nov 1995 [6] P S Hamilton and W J Tompkins, Compression of the ambulatory ECG by average beat subtraction and residual differencing, IEEE Trans Biomed Eng, vol 38, pp , Mar 1991 [7] M L Hilton, Wavelet and wavelet packet compression of electrocardiograms, IEEE Trans Biomed Eng, vol 44, May 1997 [8] M Ishijima, S B Shin, G H Hostetter, and J Sklansky, Scan along polygon approximation for data compression of electrocardiograms, IEEE Trans Biomed Eng, vol BME-30, pp , Nov 1983 [9] S M Jalaleddine and C G Hutchens, SAIES A new ECG data compression algorithm, J Clin Eng, vol 15, no 1, pp 45 51, Jan/Feb 1990 [10] S M Jalaleddine, C G Hutchens, R D Strattan, and W A Coberly, ECG data compression techniques A unified approach, IEEE Trans Biomed Eng, vol 37, pp , Apr 1990 [11] G B Moody, K Soroushian, and R G Mark, ECG data compression for tapeless ambulatory monitors, Comput Cardiol 1988, pp , 1988 [12] T Uchiyama, K Akazawa, and A Sasamori, Data compression of ambulatory ECG by using multi-template matching and residual coding, IEICE Trans Inform Syst, vol E76-D, no 12, pp , Dec 1993 [13] G Nave and A Cohen, ECG compression using long term prediction, IEEE Trans Biomed Eng, vol 40, pp , Sept 1993 [14] C Paggetti, M Lusini, M Varanini, A Taddei, and C Marchesi, A multichannel template based data compression algorithm, Comput Cardiol 1994, pp , 1994 [15] A G Ramakrishnan and S Supratim, ECG coding by wavelet-based linear prediction, IEEE Trans Biomed Eng, vol 44, Dec 1997 [16] U E Ruttiman and H V Pipberger, Compression of the ECG by prediction or interpolation and entropy encoding, IEEE Trans Biomed Eng, vol 26, pp , Nov 1979 [17] S C Tai, ECG data compression by corner detection, Med and Biol Eng and Comp, vol 30, pp , Nov 1992

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Kaufmann, 1996 [42] W J Tompkins, Biomedical Digital Signal Processing Englewood Cliffs, NJ: Prentice-Hall, 1993 Yaniv Zigel was born in Tel-Aviv, Israel, in 1970 He received the BSc and MSc degrees in electrical and computer engineering from the Ben-Gurion University, Beer-Sheva, Israel, in 1992 and in 1998, respectively He is working toward the PhD degree at the Department of Electrical and Computer Engineering of the same university From , he was a Technical Officer at the communication and computer corps in the Israeli Defense Forces (IDF) Currently, he is working as a Teaching and Research Assistant at the Department of Electrical and Computer Engineering of the Ben-Gurion University His research interests include one-dimensional signal processing, signal compression, and speech and speaker recognition Arnon Cohen was born in Haifa, Israel, in 1938 He received the BSc and MSc degrees in electrical engineering from the Technion-Israel Institute of Technology, Haifa, Israel, in 1964 and 1966, respectively, and the PhD degree in electrical and biomedical engineering, from Carnegie-Mellon University, Pittsburgh, PA, in 1970 Since 1972, he has been with the Department of Electrical and Computer Engineering, and the Biomedical Engineering Program, Ben-Gurion University, Beer-Sheva, Israel, where he is a Professor of Electrical and Biomedical Engineering His research interests are in signal processing, mainly with biomedical and speech applications He is the author of Biomedical Signal Processing, (Boca Raton, Fl: CRC, 1986) Amos Katz was born in Ramat Gan, Israel, in 1952 He received the MD degree from the Faculty of Health Sciences at Ben Gurion University of the Negev, Beer Sheva, Israel He was trained in cardiology at the Soroka Medical Center, Beer Sheva, and in electrophysiology at the St Vincent Hospital, Indianapolis, IN He is currently the Director of the Electrophysiology Laboratory at the Soroka Medical Center He is a Senior Lecturer in Cardiology in the Faculty of Health Sciences and Vice Dean for Student Affairs at Ben Gurion University His research interests are in cardiac electrophysiology, sudden death, pacemakers, implantable defibrillators, and heart rate variability