f

Physiological measurement

Detection of brainstem auditory evoked potential by adaptive filtering F. H. Y. Chan 1

F . K . Lam 1

P.W.F.

Poon z

W. Qiu 1

1 Department of Electrical & Electronic Engineering, and z Department of Physiology, The University of Hong Kong, Pokfulam Road, Hong Kong

Abstract--A method of detecting brainstem auditory evoked potential (BAEP) using adaptive signal enhancement {ASE) is proposed and tested in humans and cats. The ASE in this system estimates the signal component of the primary input, which is correlated with the reference input to the adaptive filter. The reference input is carefully designed to make an optimal and rapid estimation of the signal corrupted with noise, such as ongoing EEG. With a good choice of reference input, it is possible to track the variability of BAEP efficiently and rapidly. Moreover, the number of repetitions required could be markedly reduced and the result of the system is superior to that of ensemble averaging (EA). To detect BAEP in cats, only 30 ensemble averages are needed to obtain a reasonable reference input to the adaptive fitter, and, for humans, 350--750 ensemble averages are sufficient for a satisfactory result. Using the LMS adaptive algorithm, individual BAEP can be obtained in real-time.

Keywords--Adaptive signal enhancement, Brainstem auditory evoked potential, Convergence, Correlation coefficient Med.& Biol. Eng. & Comput., 1995, 33, 69-75

1 Introduction

THE METHODof ensemble averaging (EA) has been widely used to estimate evoked potentials from noisy background. This is based on the assumption that the response evoked by each stimulus is the same from trial to trial, and the noise, mainly ongoing EEG activity, is random and uneorrelated with the response. Averaging the responses following each stimulus will augment the signal component and reduce the noise. The improvement in signal-to-noise ratio (SNR) is proportional to the square root of the number of trials (REC;AN,I989). To detect human BAEP, thousands of averages are often required to obtain adequate noise suppression on account of the small magnitude. It is often accepted that the EA will produce a good estimation of EPs. However, in practice, identical stimuli may not necessarily generate identical EPS, The amplitude and latency can change progressively from trial to trial. Thus, the basic assumption of EA may not be always valid (DE WeERD, 1981; REGA~q, 1989; PARKER and GOPAL^N, 1987: MCGliLLEN et aL, 1985)~ Many researchers have been working on finding ways to speed up the n~asurement time and improve the SNR of EP. In our earlier attempt, the pseudo-random signal sequence method was used to speed up the measurement time by increasing the stimulus repetition rate and using the deconvolution method to separate the overlapped responses { C ~ et fd,, 1992; Lxlvl eta!., 1991). The minimum mean square error filtering technique has also been used to detect EPs (REGAIq, 1989), The Wiener filter is a powerful tool for solving such problems. If the First received26 May and.in final form 18 October 1993 @ IFMBE: 1995 Medical & B!olog|cal Engineering 8t Computing

statistical features of the signal are stationary and a priori knowledge about signal and noise can be obtained, then this technique will obtain a good estimation of signal. Unfortunately, the BAEP signal is non-stationary (DE WF.V,RD, 1981; REGAN, 1989; WIDROWet al., 1976), and no a priori knowledge can be obtained. De Weerd presented a time-varying filter to process non-stationary signals and achieved a better result. However, this method is computationally intensive and is much more complicated than EA, and therefore, it may not be easily realised in real time. On the other hand, adaptive filtering is also widely used in noise cancellation and signal enhancement (FERRARAand WIt~ROW, t981; LACUNA et al., 1992; MADHAV~,N, 1992; THaKOg, 1987; WIDROWet al., 1975)~ Laguna et al. designed an adaptive signal-impulse-correlated filter for event-related bioelectrie signals. The filter has two inputs, the primary input is the incoming recurrence of the event-related signal, and the reference input is a unit impulse sequence synchroaised with the beginning of each recurrence. If the variability of the signal is small and the SNR of recurrence is not too low (usually above 0riB), this method can obtain a satisfactory signal estimation. When the SNR of recurrence is small, as usually is the case in evoked potential measurements, it will take much longer to converge, and may not be able to track the variability of a fast-changing signal. Thakor proposed another method of adaptive filtering using one ensemble as primary input and the following one as reference input. As the SNR of the ensemble is very small, a very poor reference signal is beingused, for the adaptive filter, The SNR at filter output will therefore hardly be improved, and the distortion of the signal will also be significanf.

January 1995

89

In this paper, we present a method using an adaptive signal enhancement (ASE) technique to detect and track BAEP. The purposes of our method are to track the response variability from trial to trial and to reduce the measurement time. The algorithm can easily be performed in real time.

F r o m eqn. 1, we obtain ~

=

(so,

yk): ~- qo, + 2~o,(Sj, - yk)

--

(5)

The mean-square error IMSE) between the actual signal and the estimated one is expressed by = t ~ [ ~ ] = EECSo, - y,)-'] + e[no~d + 2E[nok(So~ -- Yk)]

(6)

2 General theory of adaptive signal enhancement

Here, n o is not related to (So - y), and thus

Fig. 1 presents a version of ASE that is suitable for detecting BAEP. There are two inputs in ASE; input channel 0 (named the primary input) contains a signal s o plus noise n o, and input channel 1 (called the reference input) contains a signal s~, related to, but not necessarily having the same waveform as, So, and an additive noise n~. The noises n o and nx are assumed to be unrelated to each other and to both signals. The adaptive filter shown in Fig. 1 iteratively adjusts its impulse response via an adaptive algorithm so that, after convergence, the difference between the filter output y and desired response d is minimised. It can be shown that the filter output is a minimum mean-square error estimate of so alone, as follows. Define the filter error output at time instant k as ek, then

E[nok(Sok -- Yt)] = 0,

~k = d~ -- y~ = So, + no, - yk

(1)

and y~ is the filter output, given by N-I

Yk =

and eqn. 6 becomes r = EEe~] = EE(sok - yk) z] + E[n2ok]

(7)

Assume that the noises n o and nt are zero mean and their variances are a.o and a.t, respectively. As E[n2oO ---, a.o, and to minimise E[e~] in eqn. 7, El(so, - yk)z] should be minimised, such that E[(sok - y,3 2] = EEsok -- s' -- n') z] = E[so~ - s') ~] - 2E[n'(so~ - s')] + ~(n '~] --, 0

(8)

As n ' = ~=-o 1 w l n . , _ ~ is not related to either s o or s', E[n'(sok - s')] = 0. After convergence, wk ---, w*, where w~' is the convergent weight, and eqn. 8 becomes E[(Sok -- yk)2] = E[(so~ -- s') 2] + E[n '2]

N-I

~_~ WiXk-, = E WiSl(k-1) i=0

i=0

= E

so,

-

WItSl(k-i )

-

i=O

+

~

w:.~_~

= s' + n'

(2)

i=0

+ E

w'nile_i) L\i~O

where N is the length of the adaptive filter, and

= E~ + Ez S' =

~

WiSl(k_i)

(3)

wint~_i~

(4)

t=0 N-1

n'= ~

If we want E[(sok -- yk)"] --, 0, then both E l and E 2 must also tend to zero, i.e. E2 =

i=O

(9)

E

w~'nt(* - 0

-"* 0 =~

Wk* ?]ltk_i) "-~ 0 /=0

i

(to) channel 0 (pdmary input)

Eqn. t0 means that the weighted average of n~ is similar to white-noise characteristics, and

1=0 N-1

=~" (r

*

wk s , ~ - o ~ Sok

(11)

If the convergence condition is met, the weighted average of sx generates a replica of s o, the signal component of the primary input. F r o m eqn. 11, we see that sa must correlate with So in some way, but not necessarily with the same waveform as %. In short, after convergence, the output of ASE optimally estimates the signal c o m p o n e n t of the primary input as long as s~ correlates closely with s 0. The closer the correlation between the reference input s~ and the signal, the better the signal estimation. This point is very important for designing the proposed ASE.

i~put)

3 Selection of algorithm and parameters #

Fig, l 70

( a ) Two-channel adaptive signal enhancer: ( b ) structure of adaptive filter; z- 1 indicates unit-delay operator

M a n y algorithms had been developed for adaptive filtering (HAvKI~, 1986; WIDgOW and STEARNS,1985). We used the well established L M S algorithm, which is simple

Medical & Biological Engineering & Computing

January 1995

and capable of achieving satisfactory performance under certain conditions. The recursive formulas are as follows: wk+ ~ = wk + 2#~k xk

(I 2)

where ek = dk -- Yk

(13)

Yk = X~k Wk = Wrk Xk

(14)

measurements, the SNR of cats is in the range - 5 - 10 db, and the SNR of humans is about - 2 0 - - 30 dB. Considering the worst situation with SNRh . . . . = - 3 0 dB and SNRca , = - 10 dB, it may require around 600 ensembles to be averaged to improve the SNR of the reference input for human BAEP, and 30 ensembles for cats.

and

The filter input vector Xk is defined as X~=[x~

xk-1

x~-2

...

XI-N+~] r

(15)

The weight vector is defined as W,=[Wo~

wlk

W2k

...

wm-,k] r

(16)

Here k is the time index, N is the number of adaptive weights, and # is the factor that controls stability and rate of convergence. Usually, p is governed by the following condition: 0 < # <~ - -

1

(17)

4 Simulation study Several computer simulations have been carried out to check the performance of our system. An actual cat BAEP which was obtained from averaging 500 ensembles of raw data of cat BAEP, was taken as the signal in this simulation. Gaussian random noise was added to this signal before it was input to the primary input of ASE. The SNR of the primary input was set to be - 1 0 dB. The reference input was taken by averaging 25 ensembles of the original data of the cat. We used a distortion index and correlation coefficient to measure the effectiveness of our method. The distortion index is defined as

NPi,

DI =

where P~, is the power of reference input. It has been proved (FER~ARA and WmROW, 1981) that the improvement in SNR at the output of ASE is proportional to the SNR at the reference input. To obtain good results with less distortion and fast adaptation, an alternative way is to reduce the noise components in the reference input. As discussed in Section 2, the reference input should be closely correlated with the signal, i.e. the BAEP in our case. In fact, the ensemble averaging provides a good reference input as the variability of amplitude and latency of BAEP is relatively small over a short observation period (D~ WEERD, 1 9 8 1 ; MADHAVAN, 1992; REGAN, 1989). We summate the first m ensembles to obtain a reference input for ASE. The primary input is the subsequent individual ensemble, i.e. the reference input m--I i=0

the primary input e~

E[(s - y)=l] El.s2] + Ely2]

(19)

where y is the output of ASE and s is the signal to be detected. The correlation coefficient between X and Yis defined by f,x, =

coy(X, Y)

(20)

where coy(X, Y) is the covariance obtained from coy(X, 10 = E { [ X -- E ( X ) ] [ Y - E(IO]}

(21)

and variance D(X) is given by D(X) = E(X 2) - [E(X)] z

(22)

Fig. 2 illustrates the adaptive procedure of ASE in the example. Fig. 2a is the primary input of ASE, composed of signals with additive Gaussian noise; Fig. 2d is the deterministic signal; Fig. 2b is the reference input; Fig. 2c gives the adaptive processing results; and Fig. 2e is the error

j = re, m + 1 , . . .

The improvement in SNR of the reference input is of the order of x/~. Moreover, the signal part of the reference input is closely related to that of the primary input. In order to determine how many ensembles should be averaged to obtain a good reference input for ASE, it is necessary to make quantitative analysis of the SNR of the actual data. The signal power obtained by EA is defined as P.~,. Here we introduce another technique called ( + / - ) averaging, which is an algorithm using addition a n d subtraction alternatively for averaging ensembles. It has been proved (DoYLe, 1975; WAL~R, 1969) that the power obtained by using ( + / - ) averaging is equal to the power of residual error of standard EA, because the deterministic signals are mainly reduced in the ( + / , ) averaging algorithm. Defining the mean power of residual error from standard averaging as P,~s~, we estimate the SNR of the original data by S N R =~ P a v ~ - P+~-

b

r

d

o 0=1

Fig, 2

(18)

P , ~ , + P+.,It has been proved (FEtu~aI~A, 1981) that the SNR of the reference input must be at least larger than unity to obtain a good improvement in SNR at the ASE output. In our Medical & Biological Engineering & Computing

January 1995

0=3

Q=5

0-7

0=9

ddapti~ proceasino; (a) signal plus additive Gaussian noise, SNR = - 10 dB; (b) ASE reference input: correlation coefficient between signal and reference input, Pu =0"745: (c) output o f ASE tracking the signal after converoence; (d) deterministic signal; (e) A S E error; Q indicates the ensemble number: when Q = 5, ASE output very similar to the zlgnal and the A S E signal distortion outFut is about 6"5% which means the cover#ence speed in this case ix about five records when the reference input is closely correlated to the Mgnal ; 20 weight.,, the inittal values o f weioht are zero; It = 0.00000003 71

that shows the difference between the signal in Fig. 2d and the output of ASE in Fig. 2c. From Fig. 2, we find that, if the reference input was properly selected such that it had close correlation with the signal, the adaptation was very fast and the accuracy was high. In our case, the correlation coefficient between the reference input and the signal was 0.745, and, after five iterations, the filter had substantially converged, giving a correlation coefficient between adapted output and the signal of 0.925, and a distortion index of 6.5%. This clearly demonstrated that the filter converged in five records. Figs. 3 and 4 show how the system tracks non-stationary signals. In Fig. 3d, the first two records (Q = 9 and 10) have a signal component s~, and the following records have another signal s~,. Here, the correlation coefficient between s, and s~, is 0"767, and the reference remains the same. From Fig. 3c, we see that the system can track signal

C

d

variation within the next interval (Q = ll), if the sl is closely correlated to SkFig. 4 shows another example of signal tracking in our system. In this case, s;, is not quite the same as Sk, as the correlation coefficient is only 0.425. When signal sk changes to s~, at Q = 31, the output of ASE produces a relatively large error (distortion index is 20%), and the filter cannot track the change of signal at once because the signal s~ is less closely correlated to Sk- In the next recurrence (Q = 32), the output has adapted to the new signal s~,, and the distortion index is decreased to 12%. As can be seen, the filter can successfully track the signal variation in such a situation within five records, and the distortion index at Q = 35 is 5-2%. It has been shown above that the filter can really work well if the reference is suitably chosen. In our case, the reference input is supplied from previous averaging of the first m ensembles. The speed of tracking for signal variation mainly depends on the degree of similarity between sk and s'k. From simulation, we can see that, if the variability of signal between one recurrence and the next is within certain limits (for example, a correlation coefficient of (>767 as illustrated above), the filter will track this variation without delay. Even if the variation is as high as a correlation coefficient of 0-5, the filter also can track the change within five records. For BAEP detection, where the variability from one trial to the succeeding trial is expected to be small, and the correlation coefficient is usually not less than 0.7, our system can effectively and rapidly track the variation of signal.

e

O,,, 9

0== 10

O = 1t

Q= 12

O= 14

Fig. 3 Results o]" tracking the uariability of signal Jrem .s~ t o s'~ with correlation coeJficient of 0.767; ( a ) siynal plus additive Gaussian noise. SNR = - 10 dB; (b) ASE reference input; (c) output o.I"ASE tracking the change of signal: (d) signal s~ (before Q = 10) and s', (after Q = 10); (e) ASE error; Q indicates the ensemble number; when Q = 11, the signal chanoes and the output of ASE can catch up with the ~'ariability o f signal immediately; in this case, the st~zats before and after change are similar with each other in high degree, p~,., = 0.767: 20 weights; 1.1= O.OfRg~)O03 &

b -__

_ .

-_

5 Adaptive signal enhancement of BAEP The adaptive filter described above has been applied to detect BAEP in humans and cats. The stimulus pulse was of 0.1 ms duration, and the click rate was 10 Hz. A 40 dB sound pressure level (SPL) was given to an anaesthetised cat, and 100 dB SPL was given to a human. The response was recorded at a sampling rate of 10 kHz. The first 10 ms of response has been processed for BAEP evaluation. During the measurement of BAEP, methods such as shielding have been used to reduce the interference of noise. The SNRs of the raw human and cat data are about - 2 0 dB and - 6 dB, respectively, in this case. Fig. 5 shows the performance of the processing of cat BAEP. Fig. 5a is the original noisy data of individual ensembles. Fig. 5b shows the reference input obtained by averaging the first 25 ensembles. Fig. 5c is the output of ASE, and Fig. 5d is the result of averaging 500 ensembles

C

d b e

0,=,30

Q=~1

Q=32

0=35

0=37

Fig. 4 Result of tracking the variabiity of 3ignat from sk to ~, with the correlation coeffident of ff425; (a) signal plus additive Gau~iam noise, S N R - - - l O d B ; (b) ASE reference input; ( c ) output of ASE tracking the change of signal; (d) signal s~ (before Q = 30) and s'~ (after Q = 30): (e) A S E error: in this ease, theoutput of ASE will take se~e~al recurrences before catching up with the change o f signal az 4 is. largely different from St (P,,s't = 0.425), but it is still hi#My related to the reference input, ( P~rwr = 0.788) ; when Q = 35,. the ,~lnal distortion of the output is 5"~;: 20 weights/# =, 0~0000003

72

-C

t,=,,i,,=ll

0

d

S

G=11

I 0 ms

0=12

0=30

0=48

0=68

Fig. 5 Adagti~ enhanced re~tt of cat BAEP (10 ms data); (a) primary ASE input: {b) ASE reference input: (c) ASE output; (d) result of lEA averaging 500ensembles: Q indicates the number a f ensemble being proce~ed: 20 weights: I~ ="0"00000003

Medical 8t Biological Engineering & Computing

January 1995

for comparison with Fig. 5c. It is evident that Fig. 5c is very similar to Fig. 5d, and the correlation coefficients between Figs. 5c and d are higher than 0-6. As mentioned above, because of the variability of amplitude and latency of BAEP, the waveforms of BAEP from trial to trial may not be the same, but should be closely correlated. Fig. 6 shows another example of ASE to track individual BAEP in cat. Fig. 7 illustrates the result of ASE of human BAEP. As the SNR of human BAEP is much poorer than that of cat, more ensembles are required for averaging to obtain a reasonable reference input. In our experiment, we average the first 200 ensembles to obtain the reference input. After convergence, the output of ASE generates a good estimation of the underlying signal from each individual ensemble. Fig. 7a is the primary input, consisting of small BAEP and high noise. Fig. 7b is the reference input after averaging of the first 200 ensembles. Fig. 7c shows output of ASE, and Fig. 7d is the result of the averaging of 1500 ensembles. As assumed above, the signal variation between each two adjacent ensembles can be seen to be very small, and therefore the adjacent BAEPs are closely correlated with each other. We may further improve the result by averaging the ASE output after convergence. This may further improve the SNR of the measured BAEP without increasing the signal acquisition time. This method is useful when the SNR of the original data is very poor. Fig. 8 shows an example of the averaged filter output in human BAEP. The total number of ensembles used in ASE is 350; the first 200 ensembles are averaged to obtain the reference input, and the rest are processed by ASE. Fig. 8a

0

5

10 ms

Fig. 8 Example of averaged output of ASE in human BAEP (10 ms data) ; (a) result of averaged ASE output of I50 ensembles: total number of ensembles used is 350: the first 200 ensembles are averaged to form the reference input; ( b ) result of EA averaginy 350 ensembles; (c) result of EA avera~ting 1500 ensemble.v; 50 weights; # = 0-000000006 is the result of averaging ASE output for 150 ensembles. Fig. 8b illustrates the result of EA using the same 350 ensembles as ASE. Fig. 8c gives the result of EA of 1500 ensembles. Comparing the three waveforms in Fig. 8, we can see that, for the same number of ensembles, ASE performs much better than EA. The result of ASE using 350 ensembles can rival that of EA averaging 1500 ensembles. Therefore, by means of ASE, it is possible to reduce the BAEP measurement time significantly.

6 Discussion b

To demonstrate the advantages and effectiveness of ASE described above, some quantitative analyses on actual data have been performed. Fig. 9 shows the comparisons of EA and ASE performance in detecting cat BAEP. Fig. 9a is the averaging residual error of ASE, i.e.

C

M

d Q=69

Q~78

Q=82

0=86

j=t

Q=125

Fig.6 Further adaptive enhanced results of cat BAEP (IOtas data) ; (a) primary ASE input: (b) ASE reference input; (e) ASE output ; (d) result of EA averaging 500 ensembles; Q indicates the number of ensemble being processed; 20 weights: # 0-00000003)

a

=

b

C

C

d

o=21

Fig.7

o-~

o=37

o=3a

Q=c~

Adaptive enhanced result of human BAEP (IOtas data); (a) primary ASE input (b) ASE reference input; (c) ASE output; (d) result of E.A averaoino 1500 ensembles, Q indicates t ~ number of ensemble being processed; 50 weights; ~=O'Ot~O000008; note that the amplitudes of (b), (c) and (d) are 'enl~roed by 4

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Fig. 9 Compa~ons of ASE and EA performance in cat BAEP (10 ms data); (a) mean residual error (MRE) of I00 ensembles using ASE; (b) MRE of 100 ensembles ushuO EA; (c) averaged ASE output of tO0 ensembles; (d) result of EA of 500 ensembles; 20 weights. # = 0"00000003; p=~= 0-096; p~ = 0"259; P~d= 0"867

Janua~/1996

73

where L is the length of each ensemble, M is the number of ensembles being processed, d is the ensemble being processed, and y is the output of ASE. In this case, L = I00 and M = I00. Fig. 9b shows the averaged residual error of EA. Taking M ensembles and averaging all of them to obtain an estimation of BAEP defined as p, then every ensemble minuses p to obtain the averaged residual error of EA, as follows:

200 ensembles (at the SNR of - 2 0 d B ) to give a comparable result with that of EA averaging 1500 ensembles. Very little extra effort is needed to complete this adaptive processing. With the 486 computer used, the computation is very fast. Furthermore, this method keeps all the raw data and allows the physician to study any segment of the data in further detail later.

M

(ee,t)k = ~ (dkj -- Pk)

k = 1, 2. . . . . L

(24)

Figs. 9c and d show the results of EA and the result of averaging the output of ASE respectively. The correlation coefficients are Pod = 0"096 and Pbd = 0"259, thus confirming that no significant trace of signal exists in Figs. 9a and b. The result of Fig. 9 shows that the residual error of ASE is much smaller than that of EA, and therefore the result of ASE is better than that of EA for the limited 100 trials. Fig. 10 illustrates the performance comparisons of EA and ASE for human BAEP. In this case, we set L = 100 and M = 500. The mean residual error of EA is much larger than that of ASE. The difference is remarkable, and the correlation coefficients are P,d = 0.164 and Pbd = 0"443. This may indicate that there are some signals still in the mean residual error of EA, which mainly contains low-frequency components, as seen in Figs. 10c and d. As the electrical activity is recorded by scalp electrodes to detect human BAEP, the SNR of the original data is very poor (about - 2 0 dB in our cases). It should be repeated at least 1000 times to achieve a good improvement of SNR using EA. The signal variation may be significant owing to habituation, fatigue and other factors during the measurement. If the ASE method is used, the variation information can be tracked, and the number of repetitions can be greatly reduced. Comparing Figs. 10a and b, we can conclude that the result of ASE is much better than that of EA, as the residual error of ASE is very small and uncorrelated with the estimated BAEP. We can further reduce the repetition of stimulus by making use of those samples that have been averaged earlier to obtain the reference input of ASE. In this case, the computer will save every response into memory during measurement and implement the adaptive processing to include those sample also. For human BAEP it only needs

7 Conclusions We have described the method of adaptive signal enhancement and used it to determine BAEPs in humans and in animals. The principal advantages of the method are that it can greatly reduce the number of stimulus repetitions and track the response variation. We have demonstrated that, to generate a good replica of a signal component of the primary input, i.e. the BAEP, the signal component of the reference input should be closely correlated to that of the primary input but not necessarily with the same waveform. The SNR of the reference input should be improved to a reasonable degree to reduce the distortion index of the filter output and to speed up the convergence. Averaging the first m ensembles is a useful and simple method to obtain a good reference input for processing event-related bioelectric signals with poor SNR. For optimal performance, the parameters of the ASE need to be properly selected. It has been shown in simulation that, if the change of signal from one recurrence to the next is not too large (their correlation coefficient is higher than 0-7, which is usually true for BAEP), the filter can track this change without delay. Using an LMS adaptive algorithm, the computation is simple and fast. With proper reference input the filter converges rapidly. For humans less than 750 ensembles (corresponding to a typical SNR of - 3 0 dB) are sufficient to obtain a satisfactory result, comparable with that of averaging more than 1500 ensembles using EA. This research shows that ASE is applicable to a real-time detection of BAEP. Acknowledgment--This project has been supported in part by University of Hong Kong research grants.

a

References

b

Fig. 10

74

Comparisons of ASE and EA performance in human BAEP (I0 ms data); (a) mean residual error (MRE) or 500 ensembles using ASE; (b) MRE of 500 ensembles uaina EA; (c) averaged ASE output of 500 ensembles; (d) result of EA of 1500 emembles; 50 weights; [t = 0 " ~ ; p_, ~ 0"164; p~ = 0"443; P~d = 0"906

Ct~A~, F. H. Y., LAM,K. F, Poolq, P. W. F. and Du, M. H. (1992): 'Measurement of human BAERs by the maximum length sequence technique." Me.d. Biol. Eng. Coraput. 30, pp. 32-40 De WEERO,J. P. C. (1981): 'A posteriori time-varying filtering of averaged evoked potential I. Introduction and conceptual basis.' Biol. Cybern., 41, pp. 211-222 DOYLE,D. J. 0975): 'Some comments on the use of Wiener filtering for the estimation of evoked potentials.' Electroe.ncep& Clin. Neurophysiol., 38, pp. 533-534 FlZXRARA,E. Jr., and Wtotow, B. (1981): 'Multichannei adaptive filtering for signal enhancement.' IEEE Tram. ASSP-29, pp. 766-770 HA'aCrN, S. (1986): 'Adaptive filter theory.' (Prentice-HaU, Inc., Englewood Cliffs, New Jersey) LAM, F. K., CHAN,F. H. Y., PeoN, P. W. F., Du, M, H. and Xu, B. 7_,. (1991): 'Visual evoked potential measurement by maximum length sequence technique." Bio-Med. Mater. & Eng. 1, pp. 91-103 LAOUNA, P., M~rE, O., Poor~, P. W., CAM~qAt, P., Rtx, H. and TaAKOR, N. T. (1992): 'Adaptive filter for event-related bioeleetric signals using an impulse correlated reference input: comparison with signal averaging techniques.' IEEE Tram., BME-39, pp. 1032-1044

Medical & Biological Engineering & Computing

January 1995

MADHAVAN, P. G. (1992): 'Minimal repetition evoked potentials by modified adaptive line enhancement.' ibid., BME-39, pp. 760-764 McG~LLEN, C. D., Au,xoN, J. I. and Yu, K. B. (1985): 'Signals and noise in evoked brain potentials.' ibid., BME-32, pp. 1012-1016 PARKER, P. A. and GOPALAN,R. (1987): 'Evoked response signal and system nonlinearity.' ibid., BME-34, pp. 771-778 REGAN, D. (1989): 'Human brain electrophysiology: evoked potentials and evoked magnetic fields in science and medicine.' (Elsevier, New York) THA~OR N. V. (1987): 'Adaptive filtering of evoked potentials.' IEEE Trans, BME-34, pp. 6-12 WALTER, D. O. (1969): 'A posteriori 'Wiener filtering' of average evoked response.' Electroenceph. Clin. Neurophysiol., Suppl. 27, pp. 61-70 WIDRow, B., GLOVER,J. R., McCooL, J. M., KAUN~TZ,J., WILLL~MS, C. S., HEARS, R. H., ZEIDLEa, C. S., DOr~G, E. Jr. and GOODLtN, R. C. (1975): 'Adaptive noise cancelling: principles and applications.' Proc. IEEE, 63, pp. t692-1716 WfDROW, B., McCooL, J. M., LAR~r,tORE, M. G. and JOHNSON, C. R. Jr. (1976): 'Stationary and nonstationary learning characteristics of the LMS adaptive filter.' Proc. IEEE, ful, pp. 1151-1162 WIDRow, B. and STEARNS,S. D. ( 1985) :'Adaptive signalprocessing. " (Prentice-Hall, Inc., Englewood Cliffs, New Jersey)

Medical & Biological Engineering & Computing

Authors" biographies W. Qiu was born in Ningbo City, China, in 1962. He received his BS in Biomedical Engineering from Zhejiang University in 1984, and completed his MSc in Electronic Engineering at the South China University of Technology in 1991. The main research interest of the team is in medical signal processing. Dr. F. H. Y. Chan was born in 1948. From 1972 to 1974, he was a postgraduate scholarship holder in Bristol University and completed his PhD in 1974. He worked for over four years in British industry before joining the University of Hong Kong in 1976. He is currently a Senior Lecturer. Dr. F. K. Lain obtained his BS~Eng.) from the University of Hong Kong, and his MS,: and PhD from' Loughborough University. After working in Britain, he returned to Hong Kong University, and is currently a Senior Lecturer. Dr. P. W. F. Poon obtained his BSc from the Chinese University of Hong Kong and his MPhil from the University of Hong Kong. He gained his PhD from Indiana University in the USA.

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