ICONIP2006

Electrogastrogram extraction using independent componentanalysis with references

Cheng Peng Æ Xiang Qian Æ Datian Ye

Received: 9 January 2007 / Accepted: 2 March 2007 / Published online: 27 March 2007

� Springer-Verlag London Limited 2007

Abstract Electrogastrogram (EGG) is a noninvasive

measurement of gastric myoelectrical activity cutaneously,

which is usually covered by strong artifacts. In this paper,

the independent component analysis (ICA) with references

was applied to separate the gastric signal from noises. The

nonlinear uncorrelatedness between the desired component

and references was introduced as a constraint. The results

show that the proposed method can extract the desired

component corresponding to gastric slow waves directly,

avoiding the ordering indeterminacy in ICA. Furthermore,

the perturbations in EGG can be suppressed effectively. In

summary, it can be a useful method for EGG analysis in

research and clinical practice.

Keywords Independent component analysis �Independent component analysis with references �Electrogastrogram

1 Introduction

Electrogastrogram (EGG) usually refers to the surface

measurement of gastric myoelectrical activity by placing

electrodes on the abdominal skin. The gastric myoelectrical

activity of healthy human is mainly composed of rhythmic

slow waves and spikes. The normal frequency of slow

waves is about 3 cycles per minute (3 cpm or 0.05 Hz). As

recorded cutaneously, the EGG presents a weighted sum-

mation of the electrical activity of various regions of the

stomach. Studies have shown that the cutaneous electrodes

can only pick up the rhythm of the slow waves but not that

of the spikes [1].

Since the first measurement of EGG in 1921, the non-

invasiveness of EGG attracted a lot of interests. A great

deal of researchers focused on the relationship between

EGG and the gastric function, expecting to take EGG as a

clinical assessment of gastric motility disorders [2, 3].

However, the real gastric signal in EGG recording is usu-

ally weak and perturbed by stronger noises. The noises are

composed of electrocardiogram (ECG), respiratory artifact,

motion artifact, electrical interference of small intestine

and the electrode-skin interface noise, etc. [1, 2]. The fre-

quency of the respiratory artifact is around 0.2–0.4 Hz,

which is close to that of slow waves. The motion artifact is

usually a broad-band signal [1, 4]. Both artifacts are almost

inevitable and can not be suppressed without affecting the

real gastric signal by conventional frequency-dominant

filter.

Plenty of signal processing techniques have been ap-

plied to improve the quality of EGG. Besides of the classic

methods such as band-pass filter, phase-locking filter, and

autoregressive modeling, several modern methods emerged

in the last a few decades were introduced, including the

adaptive filtering [5], feature extraction [4], empirical

mode decomposition [6], etc. A blind source separation

method called independent component analysis (ICA) was

introduced to separate the real gastric signal from the

multichannel EGG recordings in 1999 [7]. Successively, an

adaptive ICA method was presented and applied in EGG

C. Peng � X. Qian � D. Ye (&)

Department of Biomedical Engineering,

Tsinghua University, Beijing, China

e-mail: ydt-dea@mail.tsinghua.edu.cn

C. Peng

e-mail: pengcheng97@mails.tsinghua.edu.cn

C. Peng � X. Qian � D. Ye

Research Center of Biomedical Engineering,

Graduate School at Shenzhen, Tsinghua University,

Shenzhen, China

123

Neural Comput & Applic (2007) 16:581–587

DOI 10.1007/s00521-007-0100-3

analysis [8]; the FastICA algorithm was applied to mag-

netogastrography [9]; and a hybrid method combining ICA

and adaptive signal enhancement was used to tracking the

gastric slow waves [10].

The model of ICA assumes that the multichannel ob-

served signals are linear mixtures of several mutual inde-

pendent sources with unknown mixing coefficients. The

assumption of independence is enough to extract the

sources and estimate the demixing matrix when only ob-

served signals are available [11]. Several approaches

including maximization of nongaussianity [12–14], maxi-

mum likelihood estimation [15], minimization of mutual

information [16, 17], etc. were proved to be effective to

solve the problem. More recently, an alternative approach,

known as constrained ICA, incorporated some priori

knowledge as constraints into the model in order to elim-

inate the indeterminacy of ICA and extract the desired

components [18–20]. The priori knowledge can be tem-

poral reference signals [21, 22], as well as spatial con-

straints of the demixing matrix [23].

In this paper, an ICA model with temporal constrained

by reference signals was introduced and applied to extract

real gastric signal from EGG recording. The respiratory

and cardiac rhythms were recorded roughly by piezoelec-

tric sensor as two reference signals. The independent

component was extracted by negentropy-based method and

further constrained by nonlinear uncorrelatedness with the

reference signals. According to this method, the component

corresponding to gastric slow waves signal can be acquired

in a single one-unit ICA algorithm. Furthermore, the per-

turbation of respiratory and cardiac rhythms can be sup-

pressed more effectively than conventional ICA

approaches.

2 Method

2.1 ICA and ICA with references

The classical ICA model assumes that N channels of ob-

served signals x(t) = [ x1(t), x2(t),..., xN(t) ]T are linear

mixtures of M (usually N ‡ M) channels of mutually

independent source signals s(t) = [ s1(t), s2(t),..., sM(t) ]T:

xðtÞ ¼ AsðtÞ ð1Þ

where A is an unknown mixing matrix of N · M. In many

practical applications, x(t) are whitened during

preprocessing, so the whitened form of observations,

denoted by z(t), is considered here. The object of ICA is

to estimate the demixing matrix and the unknown sources,

denoted by W and y(t), respectively, satisfying:

yðtÞ ¼WzðtÞ ð2Þ

A flexible approximation of negentropy was introduced as

object function for one-unit ICA by Hyvarinen [13, 14]:

JðwÞ ¼ q½EfGðyÞg � EfGðmÞg�2

¼ q½EfGðwT zÞg � EfGðmÞg�2ð3Þ

where w and y specify a certain column of W and the cor-

responding component of y(t), respectively, and the time

index t is omitted for simplicity. q is a positive constant, m is a

Gaussian variable with zero mean and unit variance, and

Gð�Þ is a nonquadratic function. The object function in (3) is

further constrained by EfwT zzT wg ¼ wT wEfzT zg¼ jwj ¼ 1:

In some applications, one or more reference signals,

denoted by r(t) = [r1(t), r2(t),..., rL(t)]T, are available be-

sides the observed signals. The object function in (3) can

be further constrained by a vector of energy functions

eðy; rÞ ¼ ½eðy; r1Þ; eðy; r2Þ; . . . ; eðy; rLÞ�T ; which measures

the closeness between each reference signal and a certain

component. Hence, the ICA model with reference signals

turns out to be a problem of constrained optimization:

maximize JðwÞ;subject to eðy; rÞ6n and wk k ¼ 1

ð4Þ

where n is a vector that specifies the thresholds of each en-

ergy function. By selecting eðy; rÞ properly, a certain com-

ponent, which is ‘close to‘ or ‘far from’ the reference signals,

can be extracted. Correlation and mean square error (MSE)

were proved to be useful energy functions. In next section,

we propose an energy function based on nonlinear uncorre-

latedness, and derive a gradient learning rule to solve the

optimization problem in (4) based on augmented Lagrangian

method.

2.2 Nonlinear uncorrelatedness as a constraint

Suppose some priori information of several components,

which are considered to be perturbations, can be acquired as

reference signals. In order to extract the very component of

desired signal, it is reasonable to constrain it as far as possible

from each reference signal under a certain measurement, i.e.

uncorrelatedness or independence. In this paper, nonlinear

uncorrelatedness was introduced as a constraint in the

framework of constrained ICA.

The desired component and each reference signal are

said to be uncorrelated if:

Efðy� EfygÞðri � EfrigÞg ¼ Efyrig � EfygEfrig ¼ 0

ð5Þ

In order to find a ‘stronger’ constraint, nonlinear functions

gcð�Þ and fcð�Þ were added into (5), satisfying

582 Neural Comput & Applic (2007) 16:581–587

123

EfgcðyÞfcðriÞg � EfgcðyÞgEffcðriÞg ¼ 0 ð6Þ

The idea in (6), known as nonlinear decorrelation, was

widely used during the early research in ICA [24]. How-

ever, it can also be a measurement of ‘distance’ between

the desired component and reference signals in the sense of

nonlinear uncorrelatedness.

Assume that gc and fc have derivatives of all orders in

the neighborhood of the origin, a zero-mean form of (6)

can be rewritten and expanded in Taylor series:

EfgcðyÞfcðrÞg ¼X1

i¼1

X1

j¼1

gifjEfyirjg ¼ 0 ð7Þ

where gi and fj are coefficients of ith power in the series

and the subscript of r corresponding to the number of

reference signals is omitted here. According to Hyvarinen

et al. [11], a sufficient (but not essential) condition for (7)

to hold is that y and r are independent, and at least one of

the nonlinear functions is an odd function. Selecting gc as

such an odd function, only odd powers exist, satisfying:

Efyig ¼ 0; i ¼ 1; 3; 5; . . . ð8Þ

Under the presume that y and r should be independent

theoretically (this is because y is the exact component we

are interested in and r is a rough rhythm of a certain

perturbation), not only uncorrelatedness but also high order

uncorrelatedness of odd powers should be satisfied:

Efyirjg ¼ EfyigEfr jg ¼ 0; i ¼ 1; 3; 5; . . . ð9Þ

and the equation in (7) should be fulfilled; if not, y should

be modified iteratively according to the algorithm. As

discussed in [11], there do exist other conditions to fulfill

the equation in (7); but for nonpolynomial functions, it

seems unlikely; and in our practical applications, the

algorithm does not fall into components that are ‘closed to’

the reference signals. In this paper, an odd and sigmoid

hyperbolic tangent function widely used in previous ICA

literatures was selected as gc and fc.

Thus, incorporating with negentropy-based object

function in (3), the constrained optimization problem can

be rewritten as

Maximize JðwÞsubject to eðy;rÞ¼EfgcðyÞfcðrÞg�EfgcðyÞgEffcðrÞg6n

and wk k¼1

ð10Þ

The first constraint in (10) written in vector form reveals

that the nonlinear correlatedness of desired component and

each reference signal should be smaller than a preset

threshold. According to (10), the augmented Lagrangian is

formed as [25]:

Lðw;kÞ¼JðwÞ

þXL

i¼1

ki maxf0;eðy;riÞ�nig

þXL

i¼1

Ki

2maxf0;eðy;riÞ�nig

2

¼JðwÞþXL

i¼1

ki maxf0;eðwTz;riÞ�nig

þXL

i¼1

Ki

2maxf0;eðwT z;riÞ�nig

2

ð11Þ

where ki, i = 1,2,..., L are Lagrange multipliers and Ki, i =

1,2,..., L are the penalty parameters. The constraint |w| = 1

is not considered here because it can be easily treated by a

projection process:

w ¼ w= wk k ð12Þ

The gradient learning rule for (11) can be derived as

w ¼ w� lw

� @J

@wþXL

i¼1

Siðki þ KiðeðwT z; riÞ � niÞÞ@eðwT z; riÞ

@w

" #

ð13Þ

where

Si ¼0 if eðwT z; rÞ6n

1 if eðwT z; rÞ[n

(ð14Þ

@J

@w¼ 2qEfzgðwT zÞÞg½EfGðwT zÞg � EfGðmÞg� ð15Þ

@eðwT z; riÞ@w

¼ Efzg0cðwT zÞfcðriÞg � Efzg0cðwT zÞgEffcðriÞg

ð16Þ

g0cð�Þ is the derivative of nonlinear function gcð�Þ: The

Lagrange multipliers should also be updated as:

ki ¼ ki þ lki

@L

@ki¼ ki þ lki

ðeðwT z; riÞ � niÞ ð17Þ

The lw and lk_i in (13) and (17) are leaning rates that

should be updated as:

uw ¼1

1=uw þ wk k2ð18Þ

Neural Comput & Applic (2007) 16:581–587 583

123

uki¼ 1

1=ukiþ k2

i

ð19Þ

3 Experimental results

3.1 The measurement of EGG

The EGG data used in this paper was obtained from five

healthy humans. The subjects lay on the back and were

asked to keep quiet and as still as possible during the

measurements.

Five Ag/AgCl electrodes were placed on the abdomen,

including four active electrodes, and one reference elec-

trode (see Fig. 1). The first active electrodes was posi-

tioned 45� upper left of the midpoint between the umbilicus

and the xiphoid process with an interval of 2–3 cm, the last

active electrode was positioned 1–3 cm right to the mid-

point mentioned above. The other two were placed between

them with proper distance. The reference electrode was

positioned on the right ribs with the same height of the first

electrode. Four-channel EGG signals were derived by

connecting each active electrode to the reference electrode.

A piezoelectric sensor was placed near the umbilicus to

record the movement of the abdomen simultaneously. As

the abdomen movement is mainly caused by respiration

and heart beating, so the recorded signal is mainly con-

sisted of the respiratory and cardiac rhythms.

The signals were recorded by a multichannel physio-

logical signal recorder (RM6280C Chengdu Instrument

Factory, Chengdu, China) with a time constant of 5 s, low-

pass cutoff frequency of 10 Hz and sample frequency of

20 Hz.

3.2 Application on EGG

The raw data were decimated to 4 Hz after an anti-aliasing

filter. Furthermore, data whitening and dimension-reducing

were achieved by the principal component analysis (PCA).

Two reference signals were obtained by filtering the

recordings of the piezoelectric sensor with proper low-pass

and high-pass filters respectively (see Fig. 2). All data were

analyzed using MATLAB 6.5 by both the conventional

ICA (FastICA was used here [13, 14]) and the proposed

ICA with references. The signals shown here were regu-

lated to unit variance excepting the original recordings. A

general-purpose function G(u) = log cosh (u), proposed by

Hyvarinen in [14], was selected in (3). The selection of

thresholds in (10) is discussed in detail as follows:

In the previous work of Lin et al. [22], the threshold n

was initialized with a small value and increased gradually;

but in this paper, the EGG signals can be considered as a

same sort of signals, so it is reasonable to use an identical

threshold for each energy function in all experiments. The

identical thresholds were fixed according to one of the

experiments and the same procedure in [22] with a minor

modification, namely, the thresholds were initialized with

large values and decreased gradually. The fixed thresholds,

both 0.01 in this paper, were used in all other experiments.

Figure 3 shows a four-channel EGG recording for about

250 s. The separated components of conventional ICA and

ICA with references are shown in Fig. 4, and Fig. 5 shows

the spectra of the desired components obtained by both

methods. The components extracted by the conventional

ICA are ordered randomly, and a further step is needed to

determine which component is desired. In the ICA with

references, only one component is obtained, which is the

very component we are interested in (see Fig. 4). Theo-

retically, the two methods should extract exactly the same

desired component; but in our practical applications, the

conventional ICA gives a little ‘noisy’ component still,

which may be ascribed to the initialization of demixing

Fig. 1 The position of electrodes. Four active electrodes (a to d) and

one reference electrode (g) for EGG. A piezoelectric sensor (e) for

reference signals

Fig. 2 The reference signals with unit variance. a Corresponding to

the respiratory rhythm; b corresponding to the cardiac rhythm

584 Neural Comput & Applic (2007) 16:581–587

123

matrix and the orthonormal process. But in the ICA with

references, due to the constraint of ‘as far as possible from

the reference signals’, the perturbations of the desired

component are suppressed more effectively (see Fig. 5).

Figure 6 shows another experiment with high amplitude

disturbance. The desired component from conventional

ICA algorithm (Fig. 7b) is still perturbed by cardiac

rhythm severely; the ICA with references, however, pro-

vides a better result (Fig. 7a).

4 Conclusion and discussion

A new approach of ICA with references is presented in this

paper. The applications on EGG signals show the proposed

method can extract the desired component successfully. By

measuring the unlikeness with two reference signals in the

framework of constrained ICA algorithm, the method can

both avoid the ordering indeterminacy of conventional ICA

algorithm and suppress the perturbation effectively. This

method shows even better performance than the conven-

tional ICA when the observed data is composed with high-

amplitude disturbances, which appear in EGG recordings

frequently.

This method proves to be an improvement to the tradi-

tional extraction of gastric slow waves from the EGG

recordings. As a consequence, it will promote applications

Fig. 4 Separated components of conventional ICA (a) and ICA with

references (b) for recording in Fig. 2. All components are regulated to

unit variance

Fig. 3 Four-channel EGG recording preprocessed

Fig. 5 Spectra of components corresponding to the gastric slow

waves obtained from the conventional ICA (lower) and the ICA with

reference (upper) for recordings in Fig. 2

Fig. 6 Four-channel EGG recording with high-amplitude disturbance

in fourth channel

Neural Comput & Applic (2007) 16:581–587 585

123

of EGG in research and clinical practice, following by

further analysis on the component of slow waves.

The signal recorded by the piezoelectric sensor near

umbilicus was used firstly in the adaptive noise canceling

system [5]. Generally, the adaptive system showed good

performance in respiratory artifacts cancellation in our

previous work [26]. However, in some situations, the

adaptive method did not give the expected results. Figure 8

shows the waveform and spectrum of the first channel of

Fig. 6 after adaptive noise cancellation, which is still per-

turbed by cardiac and respiratory rhythms; and the ICA-r

method gave a better result as mentioned above (see

Fig. 7a). This may be owed to the independent assumption

in the ICA-r method, which is more ‘physiological’ for

such biomedical applications.

Acknowledgements The authors would like to thank Prof. Z. C. Wu

and his colleagues in Acupuncture Institute of China Academy of

Traditional Chinese Medicine for their assistance in acquiring the

EGG data used in this paper.

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