COMPRESSION OF MULTICHANNEL ECG USING BLIND SOURCE SEPARATION (BSS)

A. Kam and A. Cohen

Electrical and Computer Engineering Department, Ben Gurion University, Bear-Sheva, Israel.

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Abstract: In this work a new approach to multichannel ECG compression is presented. The compression is achieved using BSS algorithm, which is used to extract the independent components of the recorded ECG channels. The multichannel signal is represented as a linear combination of the independent components. Analysis by synthesis procedure is used for compression. The error signal is coded using DPCM algorithm. The transmitted signal consists of the coded error and the linear combination coefficients. The suggested algorithm was tested on a small in-house database and demonstrated comparable results to other multi-channel compression algorithms.

Introduction

With the increase of long term ECG monitoring and telemedicine, the need for efficient coding of the ECG signals increases. Many types of algorithms for single channel ECG compression have been suggested in the literature [1,2]. However only few of the algorithms deal with the problem of multichannel compression [3,4]. Multichannel compression methods have the potential to be more effective than single channel methods, due to the inter-channel correlation.

Blind Source Separation

Consider a multichannel signal :

X=[x1,x2,...,xm], xi=[xi(1),xi(2),…,xi(N)]

Assume the signal to be a linear combination of n unknown independent sources:

S=[s1,s2,...,sn], si=[si(1),si(2),.,si(N)]

The aim of the blind source separation algorithm is to produce n outputs:

Y=[y1,y2,...,yn],yi=[yi(1),yi(2),…,yi(N)]

that recreate the original source signals from the given m measured signals . In the general problem nothing is assumed about the sources except that they are statistically independent[5]. The combination system is modeled as a linear instantaneous combination. This approach assumes that the transformation from the sources to the measured signals and from the measured signals to the outputs is linear, instantaneous, and time-invariant. Under these assumptions the problem can be formulated in a matrix form:

/ (1)

A is the gain matrix where every row is the gains that creates the signal at the i’th channel (xi) by linearly combining the source vectors si. Because the only known assumption about the source signals is that they are statistically independent the matrix B is required to produceoutput signals that are statistically independent as well. This requirement is the basic idea for all BSS algorithms it is also know as Independent Component Analysis (ICA). In this paper BSS was achieved using a blind identification algorithm by Joint Approximation Diagonalization of Eigen- matrices (JADE)[6]. The scope of this paper doesn't allow getting into the details of the algorithm.

ECG multichannel compression using BSS

Clinical ECG monitoring uses 6 or 12 channels. These channels are the spatial sampling of the electric field generated by the heart muscles. Applying the multichannel signal to the JADE algorithm will provide an estimate of the independent components of the source signal s1,s2,...,sn. These components can be used as the generating base for the signal in each channel.

Using these assumptions and the fact that the inter-beat correlation is high enables the independent components of one heartbeat to approximate most of the beats. Each heartbeat will be estimated by the linear combination of the independent components of one heartbeat - S. The dimension of S is nxN where n is the number of independent components and N is the length of one heartbeat. The heartbeat length is calculated from the end of one T wave to the end of the following one. In order to allow different length to each heart beat estimated, the length of the generating components S is trimmed down or if needed stretched by adding samples in the beginning/end to each si with the amplitude of its first/last sample as required. Every heartbeat is estimated using

/ (2)

is the gain matrix estimated to best fit to X. Each row represents a channel. The error matrix (each row is the error of one channel).

/ (3)


The compression algorithm now has to transmit for each heartbeat the gaincoefficients for each channel and the coded error signal (coded and E).

The algorithm

Training phase: The estimation of the best S by the JADE algorithm[6] requires a training data of at least 20 heartbeats. Figure 1 gives an example of S estimated by the algorithm.


Figure 1 : the independent components ,S, as calculated with the JADE alg. for 8 channels.

The compression:Each new beat that will enter the system in one of the channels will be fitted with the best linear combination of S. the coefficients are estimated using steepest decent algorithm. The error signal between the original beat and the estimated signal is then coded using DPCM. Figure 2 is an example of a heartbeat of channel V2 estimated in this manner.


Figure 2: Heartbeat of channel V2 as reconstructed using S.

Testing the algorithm

The algorithm was tested with an in-house small database of 8 leads ECG recordings. The reconstructed signal was than compared to the original signal using the Percent Root mean square Difference (PRD) measure, the PRD is given by:

/ (4)

Where is the mean of the signal. The algorithm achieved PRD of 3-8% using 3 bits DPCM coding of the error signal, and yielded a bit-rate of about 800bits/sec. Figure 3 gives an example of a reconstructed beat with and without coding and the error signal (note the different scaling of the amplitude).

Figure 3. Example of one beat encoding.

Conclusion

In this paper an algorithm for ECG multichannel compression using BSS (ICA) was presented. The algorithm exploits the high inter-channel and inter-beat correlation of the ECG channel, and assumes that the signal recorded at each electrode is a transformation of a source multi-channel signal generated at one point. Initial results, on a small database, demonstrate comparable results to other multi-channel compression algorithm. We have presented here just the basic concept of how to use ICA for the compression algorithm. The algorithm can be improved considerably by using a more sophisticated coding method for the error signal and by employing a codebook of more than one beat components.

REFERENCES

[1]G. Nave and A. Cohen, “ECG compression using long term prediction,” IEEE Trans. Biomed. Eng., vol. 40, pp. 877-885, 1993.

[2] S.M.S.Jalaledine, C.G. Hutchenes, R.D. Strattan and W.A. Coberly, “ECG data compresion techniques-A unified approach,” IEEE Trans. Biomed. Eng., Vol. 37, pp. 329-343, 1990.

[3]C.P. Mammen and B. Ramamurthi, “Vector quantization for compression of multichannel ECG,” IEEE Trans. Biomed. Eng., Vol. 37, pp. 821-825, 1990.

[4]A. Cohen and Y. Zigel, “Compression of multichannel ECG through Multichannel Long-term Prediction,” IEEE Eng. In Med. and Biology Magazine, pp. 109-115,Jan/Feb 1998.

[5]C. Jutten and J. Herault, “Blind Separation of Sources, Part I: An adaptive algorithm based on neuromimetic architecture”, Signal Processing, Vol. 24, no. 1, pp. 1-10, 1991.

[6] J.-F. Cardoso, “Blind Beamforming for non Gaussian Signals,” IEE Proceedings-F, vol. 140, no. 6, pp. 362-370, 1993.