COMBINATION OF CONVOLUTIVE BLIND SIGNAL SEPARATION

AND WAVELET DECOMPOSITION TO EXTRACT THE ATRIAL

ACTIVITY IN ATRIAL FIBRILLATION

C. Vay

a, J. J. Rieta

Biomedical Synergy, Universidad Polit

ecnica de Valencia, Carretera Nazaret-Oliva s/n, 46730, Gandia, Valencia, Spain

R. Alcaraz

Universidad de Castilla-La Mancha, Camino del Pozuelo s/n, 16071 Cuenca, Spain

Keywords:

Atrial ﬁbrillation, Blind source separation, Convolutive mixture, ECG, Wavelet transform.

Abstract:

In order to use the ECG as a tool for the characterization of atrial ﬁbrillation (AF), we need to dissociate atrial

activity (AA) from ventricular activity. On the other hand, the reduced number of leads recorded from a Holter

system limits the necessary spatial diversity required by Blind Source Separation (BSS) techniques to accu-

rately extract the AA. In this work, we propose a new method, the Convolutive Multiband Blind Separation

(CMBS), to solve the problem of reduced number of leads by combining the Wavelet transform with the con-

volutive BSS algorithm Infomax. Our analysis shows up that CMBS improves the extraction performance of

AA from Holter systems in comparison with previous extraction methods. This improvement is accomplished

in two different scenarios, one for synthetic signals and another one for real signals. A high accuracy of the

estimated AA for synthetic and real AF ECG episodes is reached in both scenarios. In addition, results prove

that CMBS preserves the original AA spectral parameters.

1 INTRODUCTION

The analysis of the surface ECG is the most extended

noninvasive technique in medical diagnosis and treat-

ment of atrial ﬁbrillation (AF). In order to use the

ECG as a tool for the characterization and analysis

of AF analysis, we need to separate the atrial ac-

tivity (AA) from the ventricular activity (VA) and

other bioelectric signals (Langley et al., 2006). Given

that the spectra of AA and VA overlap, they can-

not be separated by simple linear ﬁltering, and non-

linear processing techniques must be used instead.

In this sense, Blind Source Separation (BSS) tech-

niques (Hyv

arinen et al., 2001) are able to perform a

multi-lead statistical analysis of the ECG with the aim

to obtain a set of independent sources where the AA

is included (Rieta et al., 2004). In a previous work,

we made a performance comparison of AA extrac-

tion between convolutive BSS algorithms and Inde-

pendent Component Analysis (ICA) algorithms (Vay

et al., 2007). As a main conclusion of the aforemen-

tioned work, the Infomax algorithm was the convo-

lutive BSS algorithm with the best extraction perfor-

mance, but an adjustment to the speciﬁc problem of

the AA extraction was still mandatory to improve re-

sults obtained by ICA algorithms. On the other hand,

the limited numbers of leads recorded from a Holter

system reduces excessively the necessary special di-

versity required by BSS techniques to accurately ex-

tract the AA. Consequently, other extraction tech-

niques diferent from BSS, as Average Beat Substrac-

tion (ABS) (Slocum et al., 1992), are prefered when

multi-lead ECG recordings are not available and indi-

vidual leads are used instead (Bollmann et al., 2006).

Sanchez et all partially solved this difﬁculty by in-

cluding a wavelet decomposition of Holter leads prior

to ICA analysis, what was called the Wavelet Blind

Separation (WBS) method (Snchez et al., 2004). In

this work, we present an improvement of WBS where

the ICA stage has been replaced with the convolutive

BSS algorithm Infomax (Amari et al., 1996). We will

subsequently refer to this new method as Convolutive

Multiband Blind Separation (CMBS).

373

Vayá C., J. Rieta J. and Alcaraz R. (2010).

COMBINATION OF CONVOLUTIVE BLIND SIGNAL SEPARATION AND WAVELET DECOMPOSITION TO EXTRACT THE ATRIAL ACTIVITY IN

ATRIAL FIBRILLATION.

In Proceedings of the Third International Conference on Bio-inspired Systems and Signal Processing, pages 373-376

DOI: 10.5220/0002592003730376

 SciTePress

Matrix

Synthetic leads

x [n]

Figure 1: First scenario synthetic ECG generation. Sepa-

rated AA and VA recordings of AF ECG episodes are con-

volutively mixed by the aleatory mixing matrix A.

2 DATABASE

Two different scenarios were proposed to test the AA

extraction performance of CMBS. In the ﬁrst sce-

nario, 15 pairs of separated atrial and ventricular ac-

tivities of AF episodes were mixed convolutively in

order to obtain two leads of synthesized ECGs. This

mixture was made by random mixing matrices. The

mixing process in the ﬁrst scenario can be expressed

using matrix notation as:

x[n] = A · s[n] (1)

where s[n] contains the mixed AA and VA, the s[n]

contains two synthetic ECG leads, and A is a 22 ran-

dom mixing matrix. This mixing process is schema-

tized in Fig 1 .

In the second scenario, the AA extraction perfor-

mance is analyzed on 18 real two-lead Holter record-

ings from leads V1 and V5 of AF episodes. Tree lev-

els of white additive Gaussian noise were studied in

both scenarios: no noise, a signal to noise ratio (SNR)

of 5 dB, and a SNR of 15 dB.

3 METHODS

The main difﬁculty for applying BSS techniques to

extract the AA from Holter recordings is the lack of

ECG leads. The number of observation required to

solve a BSS problem is, at least, the number of mixed

sources (Hyv

arinen et al., 2001). Given that AA,

VA, noise and other bioelectric signals are always

present in the ECG generation, two Holter leads are

not enough to determine the AA. One way to increase

the number of leads was ﬁrst introduced in the WBS

method in (Snchez et al., 2004) by the inclusion of a

wavelet decomposition stage prior to the application

of ICA. The Wavelet analysis transforms the signal

under investigation into a set of signals. These sig-

nals are called detail and approximation coefﬁcients,

each of them carrying the ECG information in differ-

ent frequency bands (Addison, 2001).

The function symlet8 with eight levels of decom-

position was used, because several wavelet fami-

lies (Addison, 2001) were tested and the best out-

comes were achieved with this conﬁguration. A

detailed description of this functions can be found

in (Addison, 2001). Detail and approximation coef-

ﬁcients were considered, so that nine observation sig-

nals resulted from each Holter lead. Consequently,

eighteen signals were used as inputs of the BSS stage.

The FastICA algorithm (Hyv

arinen et al., 2001), used

in WBS, was replaced by an infomax algorithm. The

infomax algorithms belong to an important family of

algorithms based on the information theory. Mutual

information is a natural measure of the dependence

between random signals (Hyv

arinen et al., 2001).

Asano et al proposed a BSS algorithm for convo-

lutive mixture that works in the time-frequency do-

main (Asano et al., 2001). We will subsequently refer

to this algorithm as convolutive Infomax. The general

process is illustrated in Fig 2 .

The selection of the AA from the sources esti-

mated by convolutive Infomax is made regarding to

the spectral morphology of the signals. The typical

power spectrum of AA signals contains a sharp peak

between 4 an 8 Hz and insigniﬁcant content in the

rest of frequencies (Bollmann et al., 1999). This se-

lection can be made either by visual observation of

the extracted sources spectra, or by using the Spec-

tral Concentration (SC) index, which automatizes the

decision (Castells et al., 2005). The SC will be later

deﬁned as a index that is also used to measure the per-

formance of the AA extraction.

4 PERFORMANCE INDEXES

In order to test CMBS, four performance indexes

were computed from the extracted AA in the ﬁrst sce-

nario. These indexes are the temporal correlation (R

)

with the original mixed AA, the spectral correlation

) with the Fourier transform of the original AA,

the main peak frequency ( f

), and the SC. The SC is

deﬁned as (Castells et al., 2005):

SC =

1.17 f

∑

f =0.82 f

( f )

0.5 f

∑

f =0

( f )

(2)

where P

is the power spectral density of the AA

signal, f is the frequencies vector, f

is the sampling

rate (1024 Hz), and f

is the main peak frequency

of the AA. In the second scenario, only the two last

BIOSIGNALS 2010 - International Conference on Bio-inspired Systems and Signal Processing

374

Wavelet

Decomposition

Infomax

x ,x ,...,x

21 22 29

x ,x ,...,x

11 12 19

Noise

Other

Figure 2: General CMBS process for AA extraction.

indexes were applicable since the original AA is un-

known. Good performance of AA extraction is char-

acterized by values of R

and R

near to one and high

values of SC expressed in percentage.

5 RESULTS

The results for R

in the ﬁrst scenario are shown in Fig

3. The mean values of R

obtained by CMBS (0.8526

0,8021&

0,4626&

0,2887&

0,7801&

0,7552&

0,7128&

0,8526&

0,8356&

0,7965&

0& 0,2& 0,4& 0,6& 0,8& 1&

NO&NOISE&

15&dB&

5&dB&

CMBS&

WBS&

ICA&

Figure 3: Mean R

between the original AA and the one

extracted by ICA, WBS and CMBS from synthesized ECG

recordings at three levels of SNR.

for no noise, 0.8356 for 15 dB of SNR, 0.7965 for

5 dB of SNR) are higher than mean values obtained

by WBS (0.7801 for no noise, 0.7572 for 15 dB of

SNR, 0.7128 for 5 dB of SNR) and ICA (0.8021 for

no noise, 0.4626 for 15 dB of SNR, 0.2887 for 5 dB

of SNR).

The results for R

in the ﬁrst scenario are shown

in Fig 4. The mean values of R

obtained by CMBS

0,8225&

0,6087&

0,5516&

0,7066&

0,6436&

0,6396&

0,8371&

0,8236&

0,6708&

0& 0,2& 0,4& 0,6& 0,8& 1&

NO&NOISE&

15&dB&

5&dB&

CMBS&

WBS&

ICA&

Figure 4: Mean R

between the original AA and the one

extracted by ICA, WBS and CMBS from synthesized ECG

recordings at three levels of SNR.

(0.8371 for no noise, 0.8236 for 15 dB of SNR,

0.6708 for 15 dB of SNR) are higher than those ob-

tained by WBS (0.7066 for no noise, 0.6436 for 15

dB of SNR, 0.6396 for 5 dB of SNR) or ICA (0.8225

for no noise, 0.6087 for 15 dB of SNR, 0.5516 for 5

dB of SNR).

The results for f

in the ﬁrst scenario are shown

in Fig 5. The mean f

estimated by CMBS (5.49 Hz

5,50$

5,20$

4,71$

5,65$

5,92$

3,84$

5,49$

6,07$

5,80$

0$ 1$ 2$ 3$ 4$ 5$ 6$ 7$

NO$NOISE$

15$dB$

5$dB$

(Hz)%

CMBS$

WBS$

ICA$

Figure 5: Mean f

of the AA extracted by ICA, WBS and

CMBS from synthesized ECG recordings at three levels of

SNR.

for no noise, 6.07 Hz for 15 dB of SNR, 5.80 for 5

dB of SNR) is the best approach to the mean f

of the

original mixed AA sources (5.46 Hz). Also the SC ob-

tained by CMBS (62.82% for no noise, 61.64% for 15

dB of SNR, 60.04% for 5 dB of SNR) improves the re-

sults of WBS (57.00% for no noise, 55.71% for 15 dB

of SNR, 47.61% for 5 dB of SNR) and ICA (61.78%

for no noise, 60.86% for 15 dB of SNR, 44.68% for

5 dB of SNR), and it is the best approach to the mean

SC of the mixed AA sources (62.92%). The results

for SC in the ﬁrst scenario are shown in Fig 6.

61,78&

60,86&

44,68&

57,00&

55,71&

47,61&

62,82&

61,44&

60,04&

0& 10& 20& 30& 40& 50& 60& 70&

NO&NOISE&

15&dB&

5&dB&

SC#(%)$

CMBS&

WBS&

ICA&

Figure 6: Mean SC of the AA extracted by ICA, WBS and

CMBS from synthesized ECG recordings at three levels of

SNR.

In the second scenario, the estimation of f

CMBS (5.46 Hz for no noise, 5.21 Hz for 15 dB of

SNR, 5.35 Hz for 5 dB of SNR) is less affected by

the level of noise than the estimation made by WBS

(5.24 Hz for no noise, 4.52 Hz for 15 dB of SNR, 4.77

Hz for 5 dB of SNR), and the one estimated by ICA

(5.40 Hz for no noise, 4.91 Hz for 15 dB of SNR, 4.19

Hz for 5 dB of SNR). The estimated SC values for real

Holter ECG obtained by CMBS (71.83% for no noise,

71.53% for 15 dB of SNR, 64.70% for 5 dB of SNR)

exceed the values obtained by WBS (67.13% for no

COMBINATION OF CONVOLUTIVE BLIND SIGNAL SEPARATION AND WAVELET DECOMPOSITION TO

EXTRACT THE ATRIAL ACTIVITY IN ATRIAL FIBRILLATION

375

noise, 65.18% for 15 dB of SNR, 64.32% for 5 dB of

SNR) and ICA (43.23% for no noise, 40.77% for 15

dB of SNR, 38.94% for 5 dB of SNR). The results of

and SC in the second scenario are depicted in Fig

7 and Fig 8, respectively.

5,40%%

4,91%%

4,19%%

5,24%

4,52%

4,77%

5,46%

5,21%

5,35%

0% 1% 2% 3% 4% 5% 6%

NO%NOISE%

15%dB%

5%dB%

!(Hz)!

CMBS%

WBS%

ICA%

Figure 7: Mean f

of the AA extracted by ICA, WBS and

CMBS from real ECG recordings at three levels of SNR.

43,23%

40,77%

38,94%

67,13%

65,18%

64,32%

71,83%

71,53%

64,70%

0% 10% 20% 30% 40% 50% 60% 70% 80%

NO%NOISE%

15%dB%

5%dB%

(%)$

CMBS%

WBS%

ICA%

Figure 8: Mean SC of the AA extracted by ICA, WBS and

CMBS from real ECG recordings at three levels of SNR.

6 CONCLUSIONS

Our analysis showed up that CMBS improves the ex-

traction performance of WBS and ICA in both sce-

narios so that a high accuracy of the estimated AA

for synthetic and real AF ECG episodes is accom-

plished, what is proved by the high values of R

. In

addition, the high values of R

and SC and the low

error of f

estimation prove that the original spectral

parameters of the AA are preserved in the AA esti-

mated by CMBS from both synthetic and real signals.

This fact enables CMBS as a suitable previous step to

the analysis of AA signals in the spectral domain.

ACKNOWLEDGEMENTS

This work was supported by the projects TEC2007–

64884 from the Spanish Ministry of Science and

Innovation and PAID–05–08 from the Universidad

Polit

ecnica de Valencia.

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