Quality evaluation techniques of processing the ECG signal

INTRODUCTION

In recent years, many methods of processing the Electrocardiogram (ECG) signal were reported (1), (2).

Since it is difficult to get an accurate real value of the measured property of the ECG signal due to the fluctuation of the surrounding environment effects of measuring methods used, the proposed methods are well suited to the treatment of the quality measuring method to determine and provide accurate and reliable clinical information. The accuracy of the measuring method is defined as the closeness of the real value when compared to the measured property.

The difference between real value and achieved value of measured property is known as the error.

MATERIALS AND METHODS

Brief survey of error computational method: Nearly all the problems of interest of the ECG signal processing application are suffering from error and a lacking of accuracy. The authors felt that there are need to address this particular problem to situate it within the ECG signal computational. The error consists of two scalar measures. Defined as:

[DELTA] = [V.sub.a]-[V.sub.r[??]][delta] = ([V.sub.a] - [V.sub.r])/[V.sub.r]) (1)

where, [DELTA] is the error, is the relative error, [V.sub.r] is the real value and [V.sub.a] is the achieved value. The error which repeats itself for each measurement, is called systematic error and the error which is in each measurement is different, is called random or accidental. The error related to the measurement of ECG signals (vectors) is a vector values can be represented and defined as:

[DELTA] = [V.sub.a] - [V.sub.r] (2)

where, can be considered as a discrete random function (1):

[DELTA] = [DELTA](i), i = 1,2,...N (3)

The measurement of the error can be achieved by two groups: moment and centre moment groups. These two moments are defined, respectively, as:

[m.sub.[DELTA],k] = 1/N([SIGMA][([DELTA](i)).sup.k])[[mu].sub.[DELTA],k] = 1/N([SIGMA][([DELTA](i) - [m.sub.[DELTA],l]).sup.k]) (4)

depending on k the above moments can give several statistical parameters:

* [m.sub.[DELTA]] is [[DELTA].sub.m]-mean value of the error vector,

* [m .sub.[DELTA],2]is [[DELTA].sub.mse]-mean square of the error vector,

* [[mu].sub.[DELTA],2] is [[sigma].sup.2]-the variance value of the error vector,

* ([[mu].sub.[DELTA],2).sup.1/2] in [sigma]-the standard deviation of the error vector.

The error evaluation of digital signal processing methods is used to determine the quality of these methods. This evaluation of the quality assists greatly in deciding how much the used method is useful. This research presents several methods of ECG signal processing such as filtration and detection. Many error analysis methods can be used to make sure that the processing method used are suiTable for ECG signal. The PRD algorithm was used to determine the deformation of the signal after filtering. The PRD algorithm measures error between signals interval. Thus the PRD algorithm provides information of how much the proposed method is useful (3). SNR determines the signal to noise ratio. Many other algorithms are used for ECG signal compression evaluation such as CR. In this research, two ECG models are presented: piecewise linear ECG model PL-model (1) and analytic ECG model AM (2). The ECG model signals are used for quality evaluation of ECG processing methods because the values of these signals are previously known. This makes the evaluation easier.

Piecewise linear ECG model: In this model, evaluation and processing of the ECG signal using piecewise linear model (PL-model) is achieved by time scale and amplitude scale vectors, defined respectively as:

T = [0, [T.sub.1], [T.sub.2], [T.sub.3], ... [T.sub.s]]

W = [[W.sub.0], [W.sub.1], [W.sub.2], [W.sub.3],....[W.sub.s].

Figure 1. Shows the graphical form of PL-model where the broken points or (characteristic points) determined by the above vectors with the same number of elements.

[FIGURE 1 OMITTED]

Where, N = 5. And the characteristic point:

W = [00-0.18-0.7-0.70.38-0.0500].

Figure 1 is generated using the algorithm of PL-model with amplitude resolution [2.sup.-M] and time

resolution [2.sup.-N of the ECG model signal.

The ECG signal for different beats is shown in Fig. 2 and 3.

Where, N = 8, W = [0 0 0 0 0.2 0 0 0 -0.1 1 -0.1 0 0 0.28 0 0 0 0 0 0 0.2 0 0 0 -0.1 1 -0.1 0 0 0.28 0 00 0 0 0.2 0 0 0 -0.1 1 -0.1 0 0 0.28 0 0 0 0 0 0 0.2 0 0 0 -0.1 1 -0.1 0 0 0.28 0 00 0 0 0.2 0 0 0 -0.1 1 -0.1 0 0 0.28 0 0 ]; and T=[0 30 50 60 70 80 90 110 120 130 140 150 170 190 210 220 230 250 260 270 280 290 310 320 330 340 350 370 390 410 420 430 450 460 470 480 490 510 520 530 540 550 570 590 610 620 630 650 660 670 680 690 710 720 730 740 750 770 790 810 820 830 850 860 870 880 890 910 920 930 940 950 970 990 1010 1024].

with N = 12, Wand T as in Fig. 2.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

A version of the (PL) algorithm in a detailed form:

1. Set the first value sample index i = 0 and the piece p = 1

2. calculate [t.sub.i] = [T.sub.s]/2[carrot]N*i,

3. calculate [f.sub.i](i+1) = ((W(p)-W(p-1))/(T(p)-T(p-1)))*([t.sub.i]-T(p-1))+W(p-1),