Quality evaluation of reconstructed biological signals

American Journal of Applied Sciences, Jan, 2009 by Mikhled Alfaouri, Khaled Daqrouq, Ibrahim N. Abu-Isbeih, Emad F. Khalaf

INTRODUCTION

As reported recently in literature, an increasing amount of interest of research and analysis of (ECG) has been conducted dealing with the data compression and reconstruction. The need of signal transmission over telephone lines or antenna for remote analysis, makes the compression and data reconstruction of the signal an important issue in signal processing and shed some light for researchers, many researchers were relatively reported about compression techniques and the methods were improved rapidly and gradually year after year(1), (2). An electrocardiogram (ECG) is a graphic display of the electrical activity of the heart. It provides essential information to the cardiologist to be used for the diagnostic purpose. The need of ECG signal compression exists in many transmitting of the ECG signal through telephone lines and storage applications via antennas (1). Indeed, an excellent monographic paper on this subject, explains the save of a crucial time and unnecessary difficulties in the intensive coronary care unit, or in long term 24-48 h wearable monitoring tasks (Holter's device) (3).

Memory costs may render such a solid state Holter's device impractical. If efficient compression methods are employed, memory requirements may drastically drop to make the solid state high quality Holter device commercially feasible.

On another hand, speech signal is very important biological signal that should be compressed to accomplish less size. This assists greatly in storage and transmission needs.

But, the most important stage of the original signal is the reconstruction from of the compressed data. Many methods are used for signal reconstruction for compression techniques. Inverse Fast Fourier Transform (IFFT), Inverse Wavelet Transform (IWT) and the popular techniques, decoding methods for reconstruction. The reconstruction signal quality degree determines the utilities of the given compression technique. The compression method of bad reconstruction quality is pointed as not useful, even when high compression ratio is accomplished.

The most popular method, that is used for ECG signal reconstruction quality evaluation is the Percentage Root Mean Square Difference (PRD):

PRD = [square root of [[N - 1.summation over (n = 0)][(f(n)f'[(n)).sup.2]]/[[N - 1.summation over (n = 0)]f[(n).sup.2]]]] * 100% (1)

where, f(n) is the original ECG signal and f'(n) is the reconstructed ECG signal.

Percentage root mean square difference (PRD) measures the square difference average between the original and reconstructed signals. This method determines the deformation percent in the built signal.

In (4) new method for (ECG) signal reconstruction is presented, this method based on calculating distinct errors in particular places of (ECG) signal, the chosen places are know in physiology as P-wave, Q-wave, R-wave, S-wave and T-wave as shown in Fig. 1. The error is calculated for each wave in amplitude and time duration. The errors are divided into two error simplified forms of original equations and are presented mathematically by:

[FIGURE 1 OMITTED]

WAE = [[W[A.sub.Org] - W[A.sub.Rec]]/W[A.sub.Org]]100% (2)

where, WAE is the wave amplitude error, W[A.sub.org] is the original wave amplitude and W[A.sub.rec] is the reconstructed wave amplitude and the wave time error is:

WTE = [[[WT.sub.Org] - [WT.sub.Rec]]/[WT.sub.Org]]100% (3)

where, WTE is the wave time error, [WT.sub.org] is the original wave time and [WT.sub.rec] is the reconstruction wave time.

Equation 2 and 3 calculate the relative errors, provides the relative deformation to original wave morphology. This approach needs very good detection technique of onset, offset and peak points of given wave. These points are known as fiducial points or characteristic points.

Also, percentage root mean square difference (PRD) measures the deformation in the whole signal, but this approach gives a superior measuring performance due to the exact error wave measuring in both time and amplitude domains. But the difficulties appear in fiducial point's detection of such non-stationary (ECG) signal, which varies over time rapidly very quickly. Therefore, in this research, a method that based on calculating the deformation of (DWT) coefficients of reconstruction signal, without the need of detection method as presented in (8).

In speech signal field, the reconstruction signal is valuated using other techniques. The most popular methods that are used in speech reconstruction signal (FFT), Power Spectrum Density (PSD) and Signal-to-Noise-Ratio (SNR):

SNR = 100[log.sub.10][[[N - 1.summation over (n = 0)](f'[(n)).sup.2]]]/[[N - 1.summation over (n = 0)](f(n) - f'[(n)).sup.2]]

where, f(n) is original signal and f'(n) is speech reconstructed original signal.

The most essential evaluation method for speech signal evaluation is the objective method, which based on hearing the speech of the reconstruction signal by group of people.

The proposed method in this research is based on introducing a novel modeling technique using wavelet transformation for signal error evaluation with the use of (ECG) signal as one of the most important nostationary stochastic data applications in the biomedical digital signal processing field and biological nostationary stochastic speech signal as popular signal in communication.