REVIEW OF SCIENTIFIC INSTRUMENTS 86, 035003 (2015)
Efficient block processing of long duration biotelemetric brain data for health care monitoring I. Soumya,1 M. Zia Ur Rahman,2,a) D. V. Rama Koti Reddy,3 and A. Lay-Ekuakille4
1
Department of E.I.E, GITAM University, Visakhapatnam, India Department of E.C.E, K.L. University, Vaddeswaram, Green Fields, Guntur, Andhra Pradesh, India 3 Department of Instrumentation Engineering, College of Engineering, Andhra University, Visakhapatnam, India 4 Department of Innovation Engineering, University of Salento, Lecce, Italy 2
(Received 14 November 2014; accepted 16 February 2015; published online 20 March 2015) In real time clinical environment, the brain signals which doctor need to analyze are usually very long. Such a scenario can be made simple by partitioning the input signal into several blocks and applying signal conditioning. This paper presents various block based adaptive filter structures for obtaining high resolution electroencephalogram (EEG) signals, which estimate the deterministic components of the EEG signal by removing noise. To process these long duration signals, we propose Time domain Block Least Mean Square (TDBLMS) algorithm for brain signal enhancement. In order to improve filtering capability, we introduce normalization in the weight update recursion of TDBLMS, which results TD-B-normalized-least mean square (LMS). To increase accuracy and resolution in the proposed noise cancelers, we implement the time domain cancelers in frequency domain which results frequency domain TDBLMS and FD-B-Normalized-LMS. Finally, we have applied these algorithms on real EEG signals obtained from human using Emotive Epoc EEG recorder and compared their performance with the conventional LMS algorithm. The results show that the performance of the block based algorithms is superior to the LMS counter-parts in terms of signal to noise ratio, convergence rate, excess mean square error, misadjustment, and coherence. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4913658]
I. INTRODUCTION
Neurological disorders refer to a large number of medical conditions relating to the brain functionality. These medical conditions relate to the abnormal health conditions that are directly affecting the brain and all its components. The World Health Organization (WHO) reports that neurological disorders are important cause of mortality and constitute 12% of total deaths globally. Among the neurological disorders, cerebrovascular diseases are responsible for 85% of the deaths.1–5 The electroencephalography (EEG) is a non-invasive test for measuring the brain activity dynamics graphically. When the patient is far from specialist help, biotelemetry is an effective tool for the diagnosis of brain abnormalities. The brain signal is extracted by a wearable acquisition device and the acquired signals are sent through a biotelemetry system to the hospital. Doctors analyze the received signal, decide the action to be taken, and inform the same to patient’s site for immediate action. However during acquisition, the EEG signal encounters various physiological or non-physiological artifacts. These artifacts contaminate the tiny features of brain activity which are important for clinical observation. Hence, obtaining brain activity waves without any artifacts is a high intense issue to investigate. The signal enhancement can be done in approaches, namely, non-adaptive and adaptive filterings.
a)[email protected]
0034-6748/2015/86(3)/035003/9/$30.00
However as the statistical nature of the artifacts is random, fixed coefficient filters are not suitable. In order to enhance such signals, the tap weights must adjust automatically depending on noise component. This triggers the need for efficient adaptive noise cancelers (ANCs). In a brain telemetry system, the signal recorder is interfaced with a computer to establish brain computer interface (BCI). Several BCI systems are presented in literature.6–9 Therefore, the acquisition system, biotelemetry link, BCI, and control station at the hospital establish a remote health monitoring network. In literature, several contributions on EEG enhancement using both adaptive and non-adaptive techniques were presented.10–22 Complexity reduction and fast convergence of the noise cancelation algorithm have remained a topic of intense research. This is because of the fact that with increase in the data transmission rate increases the order of filter. This causes increase in the complexity of biotelemetry system. This means that lesser time will be available to carry out the computations of filtering operation.23,24 Thus far, to the best of the authors knowledge, no effort has been made to reduce the computational complexity of the ANC in the context of brain signal enhancement. A typical Least Mean Square (LMS) based ANC has a drawback of estimating the coefficients of linear expansion.25 To overcome this problem, another approach is reported, namely, the Time Domain Block LMS (TDBLMS) algorithm.26 In this algorithm, the coefficient vector is updated only once every occurrence based on a block gradient estimation. The TDBLMS algorithm has been proposed in the case of random reference inputs
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and has, when the input is stationary, the same steady state misadjustment (MSD) and convergence speed as the LMS algorithm. However when the input data vector is large, LMS algorithm suffers from a gradient noise amplification problem. To avoid this problem, Normalized LMS (NLMS) can be used.27,28 To avoid gradient noise amplification and to achieve good filtering capability, NLMS and TDBLMS algorithms are combined, this results Time Domain Block Normalized LMS (TDBNLMS) algorithm. In order to achieve high resolution, we develop the two time domain ANCs in frequency domain for EEG enhancement. These are named as frequency domain BLMS (FDBLMS) and frequency domain BNLMS (FDBNLMS) algorithms. The advantages of these algorithms in frequency domain are low computational complexity, good accuracy, and resolution. These characteristics play a vital role in wireless biotelemetry applications. To study the performance of the ANCs, we carried our experiments on real EEG signals recorded from humans. The theory of various techniques and experimental results are presented in Secs. II and III.
II. DEVELOPMENT OF BLOCK ADAPTIVE FILTERS FOR LONG DURATION EEG SIGNALS
In practical health care environment, the duration of EEG signals is very long. This causes computational burden of signal conditioning circuit. In non-block processing, signal gets filtered sample by sample, as first in first out process. But in block processing, we divide the entire signal into small blocks and process block by block instead of sample by sample.29 This significantly reduces computational complexity of ANC. During continuous monitoring of the patient’s EEG in real time, there is a good chance for artifacts contaminating the EEG signals. The predominant artifacts are Power Line Noise (PLN), Eye Blink Artifact (EBA), ElectroMioGram (EMG), Cardiac Signal Artifact (CSA), Respiration Artifact (RA), and Electrode Motion Artifacts (EMA). All these noises mask the tiny features of the EEG signal and lead to false diagnosis. Therefore to allow the neurologist for correct diagnosis, there is need for adaptive filter for artifacts removal. Consider a length L, LMS based adaptive filter, that takes an input sequence x(n) and updates the weights as w(n + 1) = w(n) + µ x(n) e(n),
(1)
where, w(n) = [w0(n) w1(n) · · · w L−1(n)]t is the tap weight vector at the nth index, x(n) = [x(n) x(n − 1) · · · x(n − L + 1)]t , error signal e(n) = d(n) − wt (n) x(n), with d(n) being the so-called desired response available during initial training period, and µ denoting so-called step-size parameter. In order to remove the noise from the EEG signal, the EEG signal s1(n) corrupted with noise signal n1(n) is applied as the desired response d(n) for the adaptive filter. The noise signal, n2(n) possibly recorded from another generator of noise that is correlated in some way with n1(n) is applied at the input of the filter, i.e., x(n) = n2(n) the filter error becomes e(n) = [s1(n) + n1(n)] − y(n), where y(n) is the filter output given by y(n) = wt (n)x(n).
(2)
Now, the mean-squared error (MSE) becomes E[e2(n)] = E{[s1(n) − y(n)]2} + E[n12(n)].
(3)
Since s1(n) and n1(n) are uncorrelated, similarly n1(n) and y(n) are uncorrelated, the last two expectations are zero. Minimizing the MSE results in a filter output that is the best leastsquares estimate of the signal s1(n). In real time applications, the signal length is quite large and may require adaptive filters with excessively long lengths. In such cases, the conventional LMS algorithm, which is simple, is computationally expensive to implement. The block processing of the data samples can significantly reduce the computational complexity of adaptive filters.29,30 A typical block adaptive filter is shown in Fig. 1. Based on this, we have implemented various ANCs based on TDBLMS, TDBNLMS, and their frequency domain versions. In a TDBLMS based ANC, the input sequence x(n) is partitioned into nonoverlapping blocks of length P each by means of a serialto-parallel converter, and the blocks of data so produced are applied to an FIR filter of length L, one block at a time. Therefore, the adaptation proceeds on block-by-block basis.31 With the jth block, ( j ∈ Z) consisting of x( j P + r), r ∈ Z P = 0, 1, . . . , P − 1, the filter coefficients are updated from block to block as w( j + 1) = w( j) + µΣrP−1 =0 x( j P + r)e( j P + r),
(4)
where w( j) = [w0( j)w1( j) . . . w L−1( j)]t is the tap weight vector corresponding to the jth block, x( j P + r) = [x( j P + r) x( j P + r − 1) . . . x( j P + r − L + 1)]t , and e( j P + r) is the
FIG. 1. Block adaptive filter structure.
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TABLE I. A computational complexity comparison table (M = L + P − 1, r = l og2M ). Algorithm
MACs
ASC
Divisions
Shifts
LMS NLMS TDBLMS FDBLMS
L L+1 (L + 1)P + L 10Mr + 10M
Nil Nil Nil 10Mr + 2M + P
Nil 1 Nil Nil
Nil Nil (L + P) 35Mr + 18M + 2P
output error at n = j P + r, given by e( j P + r) = d( j P + r) − y( j P + r).
(5)
The sequence d( j P + r) is the so-called desired response available during the initial training period, and y( j P + r) is the filter output at n = j P + r, given as y( j P + r) = wt ( j) x( j P + r).
(6)
The parameter µ, popularly called the step size parameter, is to be chosen as 0 < µ < [P t2r R] for convergence of the algorithm. The TDBLMS suffers from the drawback of gradient noise amplification and low convergence speed. Normalized LMS (NLMS) algorithm is another class of adaptive algorithm used to train the coefficients of adaptive filter. This algorithm accounts the variation in signal level at filter output and selecting normalized step size parameter that results in a stable as well as fast converging algorithm.27 The weight update relation for NLMS algorithm is similar to that of LMS but the variable step can be written as follows: µ(n) =
µ . q + xt (n) x(n)
(7)
Here, µ is fixed convergence factor to control maladjustment. The parameter q is set to avoid denominator being too small and step size parameter too big. The normalized algorithm usually converges faster than the LMS algorithm, since it utilizes a variable convergence factor aiming at the minimization of the instantaneous output error.28 By combining TDBLMS and NLMS, we introduce TDBNLMS algorithm for brain signal enhancement. Therefore, the convergence behavior of the TDBLMS algorithm is greatly improved if we replace the scalar step-size parameter µ by µ(n) given by (7) in (4). The resultant update equation corresponds to block normalized LMS algorithm is given as w( j + 1) = w( j) + µ(n)ΣrP−1 =0 x( j P + r)e( j P + r).
(8)
A. Implementation of adaptive algorithms in frequency domain
The FDBLMS algorithm is implementation of the TDBLMS algorithm in frequency domain. The element by element multiplication of the frequency domain samples of the input and filter coefficients is followed by an Inverse Fast Fourier Transform (IFFT) and a proper windowing of the result to obtain the output vector.30 In fast algorithms, the input samples are collected in an input buffer whose output is the vector x(k), consisting of L new samples and N − 1 samples from the previous block. The vector x(k) is converted
to the frequency domain and multiplied by the associated tapweight vector, on element by element basis. This gives the samples of the filter output in the frequency domain which is subsequently converted to the time domain using an IFFT. The filter output vector as given by (6) can be realized efficiently by the overlap-save method via M = L + P − 1 point Fast Fourier Transform (FFT), where the first L − 1 points come from the previous sub-block, for which the output is to be discarded. Similarly, the weight update term in (4), viz., ΣrP−1 =0 x( j P + r)e( j P + r) can be obtained by the usual circular correlation technique, by employing M point FFT and setting the last P − 1 output terms to zero. This technique can be used for the efficient implementation FDBLMS algorithm. In this algorithm, an N-point FFT is used for the computation, where N = 2M. Thus, the N-by-1 vector is given by w( j) . W( j) = FFT (9) 0 In the above equation, 0 is the M − by − 1 null vector. Let U(j) be the diagonal matrix obtained by Fourier transforming two successive blocks of input data, d( j) be the M-by-1 desired response vector. By applying overlap-save method to the linear convolution of (2) yields the M-by-1 vector y T (k) = last M elements of IFFT [U( j)W( j)]. The error signal in frequency domain is represented as 0 . E( j) = FFT (10) e( j) Finally, the weight update recursion in (4) can be realized in frequency domain as Φ( j) . W( j + 1) = W( j) + µ FFT (11) 0 Therefore in FDBLMS, the filtering and weight updation will be done in frequency domain using FFT, i.e., convolution is efficiently done by block processing further by applying FFT for the entire block. Here, Φ( j) is a matrix of first M elements of IFFT [D( j)U( j)E( j)], where D( j) is related to diagonal matrix of average signal power, E( j) is transform of error signal vector. Similarly, TDBNLMS can be implemented in frequency domain and is given as Φ( j) . W( j + 1) = W( j) + µ(n) FFT (12) 0 This is known as FDBNLMS, where µ(n) is given same as in (7).
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TABLE II. SNRI contrast of various ANCs for EEG signal enhancement (all values in dB).
Noise
Data
LMS No.
NLMS
TD BLMS
FD BLMS
TD BNLMS
FD BNLMS
PLN
1 2 3 4 5 Avg.
7.4371 7.0642 4.6490 6.2264 5.5546 5.7928
14.7393 15.4318 11.4274 13.8090 12.5742 12.9657
8.2756 14.7095 5.6191 7.9966 6.9963 7.1233
20.2964 14.2447 17.3722 19.3153 19.0112 18.9694
15.1640 14.0526 12.9052 14.4719 13.5327 13.8322
22.9427 10.9624 19.4143 21.2030 20.9952 21.0616
EMG
1 2 3 4 5 Avg.
5.2187 7.3654 5.8436 4.8365 6.7382 6.0005
9.7810 11.5372 9.9572 8.5631 10.0863 9.9849
6.5351 8.4523 6.8437 5.4496 7.4437 6.9448
19.0728 21.3721 19.4265 18.5742 20.8732 19.8637
11.8920 13.2755 12.0264 10.6342 12.9245 12.1505
21.1257 23.4531 21.6433 20.8421 22.1791 21.8486
CSA
1 2 3 4 5 Avg.
5.5218 6.3142 7.0402 4.9953 5.9643 5.9671
9.7995 10.1151 11.2432 8.7436 9.9872 9.9777
6.5871 7.9196 8.6319 5.4537 6.8743 7.0933
18.9257 19.7341 20.5631 17.8430 19.1547 19.2441
10.8270 11.6036 12.9542 9.9647 11.0564 11.2811
21.9853 22.5631 23.4972 20.5742 22.0146 22.1268
RA
1 2 3 4 5 Avg.
4.8476 5.2387 7.1343 9.5372 6.9362 6.7388
10.3511 11.2794 13.1133 15.3562 12.7231 12.5646
5.7870 6.3254 8.5632 10.6334 7.9343 7.8486
17.1979 18.6232 20.6734 22.9454 19.0256 19.6931
12.6523 13.9342 15.0637 17.0364 14.7342 14.6841
20.7643 21.6422 23.6472 25.6241 22.6456 22.8646
EMA
1 2 3 4 5 Avg.
6.1598 5.2761 7.8021 4.7904 5.7531 5.9563
9.7091 8.7536 10.3592 7.9896 8.9342 9.1491
7.5826 6.9114 8.6429 5.8542 7.2745 7.2531
20.1917 19.3380 21.1273 18.5411 19.6972 19.7790
11.516 10.8749 9.3164 10.5967 11.2364 11.0051
22.8321 21.7127 20.4741 9.5937 21.9354 22.1414
B. Computational complexity issues
As the block based approach greatly reduces computational complexity when the input sequence is excessively large, the proposed schemes provide elegant means to remove noise from the EEG signal. Table I provides comparative account of various algorithms in terms of number of operations required. The computational complexity of TDBNLMS and FDBNLMS is similar to TDBLMS and FDBLMS except that some more computations are required for calculating variable step size. In the case of TDBNLMS, the normalized version of step size requires one division, L multiplications and accumulations (MACs) for the denominator part. By using a technique called distributive arithmetic, the denominator of normalized technique can be realized with zero multiplications.32 In our experiments in order to reduce this complexity, a block-based approach is used in which the input data are partitioned into blocks, and the maximum magnitude within each block is used to compute step size. Therefore, the computation of denominator requires only one MAC. III. SIMULATION RESULTS
To show that the proposed algorithms are really effective in clinical situations, the methods have been validated using
several EEG recordings with a wide variety of wave morphologies recorded using the Emotive EPOC headset33 which has 14 data-collecting electrodes and 2 reference electrodes. The electrodes are placed in roughly the international 10-20 system and are labeled as such.34 The headset transmits encrypted data wirelessly to a Windows-based machine; the wireless chip is proprietary and operates in the same frequency range as 802.11(2.4 GHz). Using this BCI, we have recorded brain signals with various artifacts from 5 subjects. The headset samples all channels at 128 samples/second, each of which is a 4-byte floating-point number corresponding to the voltage of a single electrode. The data rate of the EEG data streamed from the relay laptop to the mobile phone is 4 kbps per channel. In our simulation, we have recorded 200 000 samples. But due to space constraint to show high resolution signal, we have used first 1000 samples. In our experiments, we have implemented and tested adaptive filters with the three cases, i.e, (1). P = L = 10, (2). P = 5, L = 10, and (3). P = 10, L = 5. Among the three, the first case gives better performance in terms of signal to noise ratio (SNR) measurement (the results shown in this paper are for this case). For evaluating the performance of proposed filter structures, we have measured signalto-noise ratio improvement (SNRI), Excess Mean Square Error (EMSE), MSD, and Coherence (CHO) in ten experiments,
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TABLE III. Performance contrast of various ANCs for EEG signal enhancement.
Noise
Characteristics
LMS
NLMS
TD BLMS
FD BLMS
TD BNLMS
FD BNLMS
PLN
EMSE MSD CHO
−15.2858 0.0852 0.6210
−20.5372 0.0578 0.8842
−23.1546 0.0295 0.9425
−28.4315 0.0098 0.9813
−25.5496 0.0152 0.9673
−30.6431 0.0053 0.9875
EMG
EMSE MSD CHO
−18.6242 0.1164 0.6729
−23.7342 0.0852 0.8430
−26.6331 0.0645 0.8921
−31.4324 0.0326 0.9654
−28.0263 0.0429 0.9165
-33.3754 0.0295 0.9795
CSA
EMSE MSD CHO
−17.7639 0.0967 0.6462
−22.7537 0.0643 0.8636
−25.4185 0.0384 0.9372
−30.8564 0.0169 0.9684
−27.7565 0.0274 0.9527
−32.5631 0.0147 0.9857
RA
EMSE MSD CHO
−15.6793 0.0915 0.6436
−20.8540 0.0474 0.7932
−23.5975 0.0396 0.8563
−28.8164 0.0195 0.9725
−25.9647 0.0264 0.9146
−31.3659 0.0153 0.9864
EMA
EMSE MSD CHO
−16.3627 0.0984 0.6364
−21.6342 0.0685 0.8894
−24.9353 0.0427 0.9383
−29.8452 0.0256 0.9665
−26.0453 0.0315 0.9502
-31.7234 0.0175 0.9715
averaged, and compared with conventional LMS based ANC. For all the figures, the number of samples is taken on x-axis and amplitude on y-axis, unless stated. As the practical application of the proposed implementation is in biotelemetry, since the nature of channel noise is Gaussian, so to resemble channel noise in our experiments, we added a Gaussian noise with variance of 0.01. The choice of this value of variance has been performed after different trials so that the additional Gaussian noise does not determine the removal of useful information but only cancels envisaged artifacts. Such value is the optimal. However, for the case of the artwork, since we deal with EEG
signals, neurologists generally add Gaussian noise with their recording instrumentation to smooth final undesired noise. They do that empirically. As it is an adaptive system, the indicated value corresponds to the best one that produces the minimum error. Usually, with the sample amplitude as it is pointed out in the paper, acceptable values of variance range from 0.005 up to 0.02. Table II gives the SNRI contrast of various artifact eliminations. Table III gives the contrast of all algorithms in terms of EMSE, MSD, and CHO. In our experiments, we have considered a dataset of five EEG records: Record 1, Record 2,
FIG. 2. Typical brain signal enhancement results of PLN cancelation due to various ANCs: (a) EEG Signal with PLN, (b) a typical PLN, (c) LMS based ANC, (d) NLMS based ANC, (e) TDBLMS based ANC, (f) FDBLMS based ANC, (g) TDBNLMS based ANC, (h) FDBNLMS based ANC.
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These are recorded using the Emotive EPOC headset with a sampling frequency 128 samples/second. A random noise is added to the ECG signals to resemble channel noise while transmission. The input SNR for the above non-stationary noise is taken as 1.25 dB. B. Adaptive cancelation of PLN
Record 3, Record 4, and Record 5 to ensure the consistency of results. Various ANCs are implemented using LMS, NLMS, TDBLMS, FDBLMS, TDBNLMS, and FDBNLMS algorithms. Various experiments are performed to remove several artifacts from the recorded brain signals, these results are shown in Figs. 2–9, presented as follows.
This experiment demonstrates PLN cancelation. The input to the filter is EEG signal corrupted with PLN of frequency 50 Hz and sampled at 160 Hz recorded from a male person aged 41 (this signal is considered as Record 1). The reference signal is synthesized PLN; the output of the filter is recovered signal. The EMSE behavior of various ANCs is shown in Fig. 3. We have performed this experiment on five EEG records for ten times and averaged. Various performance measures like, SNRI, EMSE, MSD, CHO are tabulated in Tables II and III. Due to space constraint filtering results of record 1 are shown in this paper, it is shown in Fig. 2. In SNRI measurements, it is found that FDBNLMS algorithm gets SNRI of 22.9427 dB, FDBLMS gets 20.2964 dB, TDBNLMS gets 15.1640 dB, NLMS gets 14.7393 dB, TDBLMS gets 8.2756 dB, where as the conventional LMS algorithm improves to 7.4371 dB.
A. Noise generator
C. Adaptive cancelation of EMG
The desired signal d(n) shown in Fig. 1 is taken from noise generator. A synthetic PLN with 1 mV amplitude is generated for PLN cancelation; no harmonics are synthesized. In order to test the filtering capability in the non-stationary environment, we have considered real EMG, CSA, RA, and EMA noises.
The contaminated brain activity signal is applied as primary input to the adaptive filter of Fig. 1; reference signal is taken from our noise generator. This noise generator design synthesizes various artifacts which are in some way correlated with the power spectral distribution of noise component
FIG. 3. A typical EMSE behavior for the removal of PLN from brain signals.
FIG. 4. Typical brain signal enhancement results of EMG cancelation due to various ANCs: (a) EEG Signal with EMG, (b) a typical EMG artifact, (c) LMS based ANC, (d) NLMS based ANC, (e) TDBLMS based ANC, (f) FDBLMS based ANC, (g) TDBNLMS based ANC, (h) FDBNLMS based ANC.
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FIG. 5. Typical brain signal enhancement results of CSA cancelation due to various ANCs: (a) EEG Signal with CSA, (b) a typical CSA, (c) LMS based ANC, (d) NLMS based ANC, (e) TDBLMS based ANC, (f) FDBLMS based ANC, (g) TDBNLMS based ANC, (h) FDBNLMS based ANC.
present in the input signal. This noise generator has different types of artifacts which can be used as reference signals in enhancement process. The adaptive filter has an innate ability to change its coefficients, so that the reference signal made equivalent to noise component in the input signal. The simulation results for record 1 are plotted in Fig. 4. From the performance measure tabulated in Tables II and III, it is clear that NLMS based noise canceler performs better than other algorithms. In SNRI measurements, it is found that FDBNLMS algorithm gets SNRI of 21.1257 dB, FDBLMS gets 19.0728 dB, TDBNLMS gets 11.8920 dB, NLMS gets 9.7810 dB, TDBLMS gets 6.5351 dB, where as the conventional LMS algorithm improves to 5.2187 dB. D. Adaptive cancelation of CSA
physiological artifact in the EEG signal. In our experiments, we performed the cancelation of such artifact from brain activity. The output signals from various ANCs based on mean square approach are shown in Fig. 7. Various performance measuring characteristics are tabulated in Tables II and III. In SNRI measurements, it is found that FDBNLMS algorithm gets SNRI of 20.7543 dB, FDBLMS gets 17.1979 dB, TDBNLMS gets 12.6523 dB, NLMS gets 10.3511 dB, TDBLMS gets 5.7870 dB, where as the conventional LMS algorithm improves to 4.8476 dB. F. Adaptive cancelation of EMA
In this experiment, the noisy EEG signal is given to ANC structure shown in Fig. 1; the reference is taken from noise
During acquisition of EEG signal, cardiac signal contaminates the brain potential. This results in high amplitude cardiac activity in brain activity signal. For better analysis of EEG signal, we apply EEG with CSA to various ANCs designed based on mean square approach. The filtered signals are shown in Fig. 5; the EMSE curves are shown in Fig. 6. Various performance measuring characteristics are tabulated in Tables II and III. In SNRI measurements, it is found that FDBNLMS algorithm gets SNRI of 21.9853 dB, FDBLMS gets 18.7257 dB, TDBNLMS gets 10.8270 dB, NLMS gets 9.7995 dB, TDBLMS gets 6.5871 dB, where as the conventional LMS algorithm improves to 5.5218 dB. E. Adaptive cancelation of RA
Because of the patients breathing activity, the base line of the EEG signal wanders up and down, causes some
FIG. 6. A typical EMSE behavior for the removal of CSA from brain signals.
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FIG. 7. Typical brain signal enhancement results of RA cancelation due to various ANCs: (a) EEG Signal with RA, (b) a typical RA, (c) LMS based ANC, (d) NLMS based ANC, (e) TDBLMS based ANC, (f) FDBLMS based ANC, (g) TDBNLMS based ANC, (h) FDBNLMS based ANC.
generator. Noise free brain signals after the elimination of EMA are shown in Fig. 8; the EMSE curves are shown in Fig. 9. Various performance measuring characteristics are tabulated in Tables II and III. In SNRI measurements, it is
found that FDBNLMS algorithm gets SNRI of 22.8321 dB, FDBLMS gets 20.1917 dB, TDBNLMS gets 11.5160 dB, NLMS gets 9.7091 dB, TDBLMS gets 7.5826 dB, where as the conventional LMS algorithm improves to 6.1598 dB.
FIG. 8. Typical brain signal enhancement results of EMA cancelation due to various ANCs: (a) EEG Signal with EMA, (b) a typical EMA, (c) LMS based ANC, (d) NLMS based ANC, (e) TDBLMS based ANC, (f) FDBLMS based ANC, (g) TDBNLMS based ANC, (h) FDBNLMS based ANC.
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FIG. 9. A typical EMSE behavior for the removal of EMA from brain signals.
IV. CONCLUSION
In this paper, the process of artifact removal from EEG signals corrupted by various artifacts using block based adaptive filters in both time and frequency domains was presented. The various filter structures based on TDBLMS, FDBLMS, TDBNLMS, and FDBNLMS algorithms are developed for EEG noise cancelation. For this, the input and the desired response signals are properly chosen in such a way that the filter output is the best least squared estimate of the original EEG signal. The proposed treatment exploits the modifications in the weight update formula and thus pushes up the speed over the respective LMS based realizations. From the simulation results, it is clear that the tracking capability of these algorithms in presence of non-stationary noise environment is better. Our simulations, however, confirm that the SNRI of the block filters is better than that of LMS algorithm. Also, the computational complexity of frequency domain filters is less than that of their time domain implementations. Hence, these systems are well suited for biotelemetric brain data analysis. 1Atlas:
Epilepsy Care in the World (World Health Organization, Geneva, 2005). 2Neurological Disorders: Public Health Challenges (World Health Organization, Geneva, 2006). 3Disease Control Priorities Related To Mental, Neurological, Developmental And Substance Abuse Disorders (World Health Organization, Geneva, 2006). 4Brain and Eye Disease Researcher Survey (Bright Focus Foundation, 2012). 5Neurological Diseases and Neuroscience (World Health Organization, Geneva, 2000). 6A. Nijholt and D. Tan, “Brain-computer interfacing for intelligent systems,” IEEE Intell. Syst. 23(3), 72–79 (2008). 7B. J. Lance, S. E. Kerick, A. J. Ries, K. S. Oie, and K. McDowell, “Brain computer interface technologies in the coming decades,” Proc. IEEE 100, 1585–1599 (2012). 8J. B. F. Van Erp, F. Lotte, and M. Tangermann, “Brain computer interfaces: Beyond medical applications,” IEEE Comput. Soc. 45(4), 26–34 (2012). 9G. Schalk and E. C. Leuthardt, “Brain computer interfaces using electrocorticographic signals,” IEEE Rev. Biomed. Eng. 4, 140–154 (2011). 10H. Higashi and T. Tanaka, “Simultaneous design of FIR filter banks and spatial patterns for EEG signal classification,” IEEE Trans. Biomed. Eng. 60(4), 1100–1110 (2013).
S. Zandi, G. A. Dumont, M. J. Yedlin, P. Lapeyrie, C. Sudre, and S. Gaffet, “Scalp EEG acquisition in a low-noise environment: A quantitative assessment,” IEEE Trans. Biomed. Eng. 58(8), 2407–2417 (2011). 12N. Mammone, D. Labate, A. Lay Ekuakille, and F. C. Morabito, “Analysis of absence seizure generation using EEG spatial temporal regularity measures,” Int. J. Neural Syst. 22(6), 1250024 (2012). 13D. Labate, F. La Foresta, G. Occhiuto, F. C. Morabito, A. Lay-Ekuakille, and P. Vergallo, “Empirical mode decomposition vs. wavelet decomposition for the extraction of respiratory signal from single-channel ECG: A comparison,” IEEE Sens. J. 13(7), 2666–2674 (2013). 14A. Lay-Ekuakille, P. Vergallo, A. Trabacca, M. De Rinaldis, F. Angelillo, F. Conversano, and S. Casciaro, “Low-Frequency detection in ECG signals and joint EEG-Ergospirometric measurements for precautionary diagnosis, measurement,” J. Meas. 46(1), 97–107 (2013). 15A. Lay-Ekuakille, P. Vergallo, G. Griffo, F. Conversano, S. Casciaro, S. Urooj, V. Bhateja, and A. Trabacca, “Mutidimensional Analysis of EEG Features using Advanced Spectral Estimates for Diagnosis Accuracy,” in 2013 IEEE International Symposium on Medical Measurements and Application, Canada, May, 2013. 16N. Mammone, A. Lay-Ekuakille, C. Morabito, A. Massaro, S. Casciaro, and A. Trabacca, “Analysis of absence seizure EEG via Permutation Entropy spatio-temporal clustering,” in 2011 IEEE International Symposium on Medical Measurements and Application, Bari, May, 2011. 17Z. Zhilin, J. Tzyy-Ping, S. Makeig, and B. D. Rao, “Compressed sensing of EEG for wireless telemonitoring with low energy consumption and inexpensive hardware,” IEEE Trans. Biomed. Eng. 60(1), 221–224 (2013). 18P. C. Petrantonakis and L. J. Hadjileontiadis, “Adaptive emotional information retrieval from EEG signals in the time-frequency domain,” IEEE Trans., Signal Process. 60(5), 2604–2616 (2012). 19I. Daly, M. Billinger, R. Scherer, and G. Muller-Putz, “On the automated removal of artifacts related to head movement from the EEG,” IEEE Trans., Neural Syst. Rehabil. Eng. 21(3), 427–434 (2013). 20B. Noureddin, P. D. Lawrence, and G. E. Birch, “Online removal of eye movement and nlink EEG artifacts using a high-speed eye tracker,” IEEE Trans. Biomed. Eng. 59(8), 2103–2110 (2012). 21H. Peng, B. Hu, Q. Shi, M. Ratcliffe, Q. Zhao, Y. Qi, and G. Gao, “Removal of ocular artifacts in EEG - An improved approach combining DWT and ANC for portable applications,” IEEE J. Biomed. Health Inf. 17(3), 600–607 (2013). 22S. Sanei, S. Ferdowsi, K. Nazarpour, and A. Cichocki, “Advances in electroencephalography signal processing,” Signal Process. Mag., IEEE 30(1), 170–176 (2013). 23M. Z. U. Rahman, S. R. Ahamed, and D. V. R. K. Reddy, “Efficient sign based normalized adaptive filtering techniques for cancelation of artifacts in ECG signals: Application to wireless biotelemetry,” Signal Process. 91, 225–239 (2011). 24M. Z. U. Rahman, S. R. Ahamed, and D. V. R. K. Reddy, “Efficient and simplified adaptive noise cancellers for ECG sensor based remote health monitoring,” IEEE Sens. J. 12(3), 566–573 (2012). 25S. Olmos and P. Laguna, “Steady-state MSE convergence analysis in LMS adaptive filters with deterministic reference inputs for biomedical signals,” IEEE Trans. Signal Process. 48, 2229–2241 (2000). 26S. Olmos, L. Sornmo, and P. Laguna, “Block adaptive filter with deterministic reference inputs for event-related signals: BLMS and BRLS,” IEEE Trans. Signal Process. 50, 1102–1112 (2002). 27S. C. Douglas, “A family of normalized LMS algorithms,” IEEE Signal Process. Lett. 1, 1352–1365 (1994). 28A. H. Sayed, Adaptive Filters (John Wiley and Sons, Inc, Hoboken, New Jersey, 2008). 29B. Farhang-Boroujeny and K. Sann Chan, “Analysis of the frequencydomain block LMS algorithm,” IEEE Trans. Signal Process. 48(8), 2332–2342 (2000). 30B. Farhang-Boroujeny, Adaptive Filters-Theory and Applications (John Wiley and Sons, Chichester, UK, 1998). 31S. Haykin, Adaptive Filter Theory (Eaglewood Clirs, NJ:Prentice-Hall, 1986). 32K. K. Parhi, VLSI Digital Signal Processing Systems (John Wiley and Sons, Inc., 1999). 33Emotiv Systems, “Emotiv brain computer interface technology,” http:// emotiv.com. 34J. Malmivuo and R. Plonsey, in Bioelectromagnetism -Principles and applications of bioelectric and biomagnetic fields (Oxford University Press, 1995).
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Efficient block processing of long duration biotelemetric brain data for health care monitoring I. Soumya,1 M. Zia Ur Rahman,2,a) D. V. Rama Koti Reddy,3 and A. Lay-Ekuakille4
1
Department of E.I.E, GITAM University, Visakhapatnam, India Department of E.C.E, K.L. University, Vaddeswaram, Green Fields, Guntur, Andhra Pradesh, India 3 Department of Instrumentation Engineering, College of Engineering, Andhra University, Visakhapatnam, India 4 Department of Innovation Engineering, University of Salento, Lecce, Italy 2
(Received 14 November 2014; accepted 16 February 2015; published online 20 March 2015) In real time clinical environment, the brain signals which doctor need to analyze are usually very long. Such a scenario can be made simple by partitioning the input signal into several blocks and applying signal conditioning. This paper presents various block based adaptive filter structures for obtaining high resolution electroencephalogram (EEG) signals, which estimate the deterministic components of the EEG signal by removing noise. To process these long duration signals, we propose Time domain Block Least Mean Square (TDBLMS) algorithm for brain signal enhancement. In order to improve filtering capability, we introduce normalization in the weight update recursion of TDBLMS, which results TD-B-normalized-least mean square (LMS). To increase accuracy and resolution in the proposed noise cancelers, we implement the time domain cancelers in frequency domain which results frequency domain TDBLMS and FD-B-Normalized-LMS. Finally, we have applied these algorithms on real EEG signals obtained from human using Emotive Epoc EEG recorder and compared their performance with the conventional LMS algorithm. The results show that the performance of the block based algorithms is superior to the LMS counter-parts in terms of signal to noise ratio, convergence rate, excess mean square error, misadjustment, and coherence. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4913658]
I. INTRODUCTION
Neurological disorders refer to a large number of medical conditions relating to the brain functionality. These medical conditions relate to the abnormal health conditions that are directly affecting the brain and all its components. The World Health Organization (WHO) reports that neurological disorders are important cause of mortality and constitute 12% of total deaths globally. Among the neurological disorders, cerebrovascular diseases are responsible for 85% of the deaths.1–5 The electroencephalography (EEG) is a non-invasive test for measuring the brain activity dynamics graphically. When the patient is far from specialist help, biotelemetry is an effective tool for the diagnosis of brain abnormalities. The brain signal is extracted by a wearable acquisition device and the acquired signals are sent through a biotelemetry system to the hospital. Doctors analyze the received signal, decide the action to be taken, and inform the same to patient’s site for immediate action. However during acquisition, the EEG signal encounters various physiological or non-physiological artifacts. These artifacts contaminate the tiny features of brain activity which are important for clinical observation. Hence, obtaining brain activity waves without any artifacts is a high intense issue to investigate. The signal enhancement can be done in approaches, namely, non-adaptive and adaptive filterings.
a)[email protected]
0034-6748/2015/86(3)/035003/9/$30.00
However as the statistical nature of the artifacts is random, fixed coefficient filters are not suitable. In order to enhance such signals, the tap weights must adjust automatically depending on noise component. This triggers the need for efficient adaptive noise cancelers (ANCs). In a brain telemetry system, the signal recorder is interfaced with a computer to establish brain computer interface (BCI). Several BCI systems are presented in literature.6–9 Therefore, the acquisition system, biotelemetry link, BCI, and control station at the hospital establish a remote health monitoring network. In literature, several contributions on EEG enhancement using both adaptive and non-adaptive techniques were presented.10–22 Complexity reduction and fast convergence of the noise cancelation algorithm have remained a topic of intense research. This is because of the fact that with increase in the data transmission rate increases the order of filter. This causes increase in the complexity of biotelemetry system. This means that lesser time will be available to carry out the computations of filtering operation.23,24 Thus far, to the best of the authors knowledge, no effort has been made to reduce the computational complexity of the ANC in the context of brain signal enhancement. A typical Least Mean Square (LMS) based ANC has a drawback of estimating the coefficients of linear expansion.25 To overcome this problem, another approach is reported, namely, the Time Domain Block LMS (TDBLMS) algorithm.26 In this algorithm, the coefficient vector is updated only once every occurrence based on a block gradient estimation. The TDBLMS algorithm has been proposed in the case of random reference inputs
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and has, when the input is stationary, the same steady state misadjustment (MSD) and convergence speed as the LMS algorithm. However when the input data vector is large, LMS algorithm suffers from a gradient noise amplification problem. To avoid this problem, Normalized LMS (NLMS) can be used.27,28 To avoid gradient noise amplification and to achieve good filtering capability, NLMS and TDBLMS algorithms are combined, this results Time Domain Block Normalized LMS (TDBNLMS) algorithm. In order to achieve high resolution, we develop the two time domain ANCs in frequency domain for EEG enhancement. These are named as frequency domain BLMS (FDBLMS) and frequency domain BNLMS (FDBNLMS) algorithms. The advantages of these algorithms in frequency domain are low computational complexity, good accuracy, and resolution. These characteristics play a vital role in wireless biotelemetry applications. To study the performance of the ANCs, we carried our experiments on real EEG signals recorded from humans. The theory of various techniques and experimental results are presented in Secs. II and III.
II. DEVELOPMENT OF BLOCK ADAPTIVE FILTERS FOR LONG DURATION EEG SIGNALS
In practical health care environment, the duration of EEG signals is very long. This causes computational burden of signal conditioning circuit. In non-block processing, signal gets filtered sample by sample, as first in first out process. But in block processing, we divide the entire signal into small blocks and process block by block instead of sample by sample.29 This significantly reduces computational complexity of ANC. During continuous monitoring of the patient’s EEG in real time, there is a good chance for artifacts contaminating the EEG signals. The predominant artifacts are Power Line Noise (PLN), Eye Blink Artifact (EBA), ElectroMioGram (EMG), Cardiac Signal Artifact (CSA), Respiration Artifact (RA), and Electrode Motion Artifacts (EMA). All these noises mask the tiny features of the EEG signal and lead to false diagnosis. Therefore to allow the neurologist for correct diagnosis, there is need for adaptive filter for artifacts removal. Consider a length L, LMS based adaptive filter, that takes an input sequence x(n) and updates the weights as w(n + 1) = w(n) + µ x(n) e(n),
(1)
where, w(n) = [w0(n) w1(n) · · · w L−1(n)]t is the tap weight vector at the nth index, x(n) = [x(n) x(n − 1) · · · x(n − L + 1)]t , error signal e(n) = d(n) − wt (n) x(n), with d(n) being the so-called desired response available during initial training period, and µ denoting so-called step-size parameter. In order to remove the noise from the EEG signal, the EEG signal s1(n) corrupted with noise signal n1(n) is applied as the desired response d(n) for the adaptive filter. The noise signal, n2(n) possibly recorded from another generator of noise that is correlated in some way with n1(n) is applied at the input of the filter, i.e., x(n) = n2(n) the filter error becomes e(n) = [s1(n) + n1(n)] − y(n), where y(n) is the filter output given by y(n) = wt (n)x(n).
(2)
Now, the mean-squared error (MSE) becomes E[e2(n)] = E{[s1(n) − y(n)]2} + E[n12(n)].
(3)
Since s1(n) and n1(n) are uncorrelated, similarly n1(n) and y(n) are uncorrelated, the last two expectations are zero. Minimizing the MSE results in a filter output that is the best leastsquares estimate of the signal s1(n). In real time applications, the signal length is quite large and may require adaptive filters with excessively long lengths. In such cases, the conventional LMS algorithm, which is simple, is computationally expensive to implement. The block processing of the data samples can significantly reduce the computational complexity of adaptive filters.29,30 A typical block adaptive filter is shown in Fig. 1. Based on this, we have implemented various ANCs based on TDBLMS, TDBNLMS, and their frequency domain versions. In a TDBLMS based ANC, the input sequence x(n) is partitioned into nonoverlapping blocks of length P each by means of a serialto-parallel converter, and the blocks of data so produced are applied to an FIR filter of length L, one block at a time. Therefore, the adaptation proceeds on block-by-block basis.31 With the jth block, ( j ∈ Z) consisting of x( j P + r), r ∈ Z P = 0, 1, . . . , P − 1, the filter coefficients are updated from block to block as w( j + 1) = w( j) + µΣrP−1 =0 x( j P + r)e( j P + r),
(4)
where w( j) = [w0( j)w1( j) . . . w L−1( j)]t is the tap weight vector corresponding to the jth block, x( j P + r) = [x( j P + r) x( j P + r − 1) . . . x( j P + r − L + 1)]t , and e( j P + r) is the
FIG. 1. Block adaptive filter structure.
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TABLE I. A computational complexity comparison table (M = L + P − 1, r = l og2M ). Algorithm
MACs
ASC
Divisions
Shifts
LMS NLMS TDBLMS FDBLMS
L L+1 (L + 1)P + L 10Mr + 10M
Nil Nil Nil 10Mr + 2M + P
Nil 1 Nil Nil
Nil Nil (L + P) 35Mr + 18M + 2P
output error at n = j P + r, given by e( j P + r) = d( j P + r) − y( j P + r).
(5)
The sequence d( j P + r) is the so-called desired response available during the initial training period, and y( j P + r) is the filter output at n = j P + r, given as y( j P + r) = wt ( j) x( j P + r).
(6)
The parameter µ, popularly called the step size parameter, is to be chosen as 0 < µ < [P t2r R] for convergence of the algorithm. The TDBLMS suffers from the drawback of gradient noise amplification and low convergence speed. Normalized LMS (NLMS) algorithm is another class of adaptive algorithm used to train the coefficients of adaptive filter. This algorithm accounts the variation in signal level at filter output and selecting normalized step size parameter that results in a stable as well as fast converging algorithm.27 The weight update relation for NLMS algorithm is similar to that of LMS but the variable step can be written as follows: µ(n) =
µ . q + xt (n) x(n)
(7)
Here, µ is fixed convergence factor to control maladjustment. The parameter q is set to avoid denominator being too small and step size parameter too big. The normalized algorithm usually converges faster than the LMS algorithm, since it utilizes a variable convergence factor aiming at the minimization of the instantaneous output error.28 By combining TDBLMS and NLMS, we introduce TDBNLMS algorithm for brain signal enhancement. Therefore, the convergence behavior of the TDBLMS algorithm is greatly improved if we replace the scalar step-size parameter µ by µ(n) given by (7) in (4). The resultant update equation corresponds to block normalized LMS algorithm is given as w( j + 1) = w( j) + µ(n)ΣrP−1 =0 x( j P + r)e( j P + r).
(8)
A. Implementation of adaptive algorithms in frequency domain
The FDBLMS algorithm is implementation of the TDBLMS algorithm in frequency domain. The element by element multiplication of the frequency domain samples of the input and filter coefficients is followed by an Inverse Fast Fourier Transform (IFFT) and a proper windowing of the result to obtain the output vector.30 In fast algorithms, the input samples are collected in an input buffer whose output is the vector x(k), consisting of L new samples and N − 1 samples from the previous block. The vector x(k) is converted
to the frequency domain and multiplied by the associated tapweight vector, on element by element basis. This gives the samples of the filter output in the frequency domain which is subsequently converted to the time domain using an IFFT. The filter output vector as given by (6) can be realized efficiently by the overlap-save method via M = L + P − 1 point Fast Fourier Transform (FFT), where the first L − 1 points come from the previous sub-block, for which the output is to be discarded. Similarly, the weight update term in (4), viz., ΣrP−1 =0 x( j P + r)e( j P + r) can be obtained by the usual circular correlation technique, by employing M point FFT and setting the last P − 1 output terms to zero. This technique can be used for the efficient implementation FDBLMS algorithm. In this algorithm, an N-point FFT is used for the computation, where N = 2M. Thus, the N-by-1 vector is given by w( j) . W( j) = FFT (9) 0 In the above equation, 0 is the M − by − 1 null vector. Let U(j) be the diagonal matrix obtained by Fourier transforming two successive blocks of input data, d( j) be the M-by-1 desired response vector. By applying overlap-save method to the linear convolution of (2) yields the M-by-1 vector y T (k) = last M elements of IFFT [U( j)W( j)]. The error signal in frequency domain is represented as 0 . E( j) = FFT (10) e( j) Finally, the weight update recursion in (4) can be realized in frequency domain as Φ( j) . W( j + 1) = W( j) + µ FFT (11) 0 Therefore in FDBLMS, the filtering and weight updation will be done in frequency domain using FFT, i.e., convolution is efficiently done by block processing further by applying FFT for the entire block. Here, Φ( j) is a matrix of first M elements of IFFT [D( j)U( j)E( j)], where D( j) is related to diagonal matrix of average signal power, E( j) is transform of error signal vector. Similarly, TDBNLMS can be implemented in frequency domain and is given as Φ( j) . W( j + 1) = W( j) + µ(n) FFT (12) 0 This is known as FDBNLMS, where µ(n) is given same as in (7).
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TABLE II. SNRI contrast of various ANCs for EEG signal enhancement (all values in dB).
Noise
Data
LMS No.
NLMS
TD BLMS
FD BLMS
TD BNLMS
FD BNLMS
PLN
1 2 3 4 5 Avg.
7.4371 7.0642 4.6490 6.2264 5.5546 5.7928
14.7393 15.4318 11.4274 13.8090 12.5742 12.9657
8.2756 14.7095 5.6191 7.9966 6.9963 7.1233
20.2964 14.2447 17.3722 19.3153 19.0112 18.9694
15.1640 14.0526 12.9052 14.4719 13.5327 13.8322
22.9427 10.9624 19.4143 21.2030 20.9952 21.0616
EMG
1 2 3 4 5 Avg.
5.2187 7.3654 5.8436 4.8365 6.7382 6.0005
9.7810 11.5372 9.9572 8.5631 10.0863 9.9849
6.5351 8.4523 6.8437 5.4496 7.4437 6.9448
19.0728 21.3721 19.4265 18.5742 20.8732 19.8637
11.8920 13.2755 12.0264 10.6342 12.9245 12.1505
21.1257 23.4531 21.6433 20.8421 22.1791 21.8486
CSA
1 2 3 4 5 Avg.
5.5218 6.3142 7.0402 4.9953 5.9643 5.9671
9.7995 10.1151 11.2432 8.7436 9.9872 9.9777
6.5871 7.9196 8.6319 5.4537 6.8743 7.0933
18.9257 19.7341 20.5631 17.8430 19.1547 19.2441
10.8270 11.6036 12.9542 9.9647 11.0564 11.2811
21.9853 22.5631 23.4972 20.5742 22.0146 22.1268
RA
1 2 3 4 5 Avg.
4.8476 5.2387 7.1343 9.5372 6.9362 6.7388
10.3511 11.2794 13.1133 15.3562 12.7231 12.5646
5.7870 6.3254 8.5632 10.6334 7.9343 7.8486
17.1979 18.6232 20.6734 22.9454 19.0256 19.6931
12.6523 13.9342 15.0637 17.0364 14.7342 14.6841
20.7643 21.6422 23.6472 25.6241 22.6456 22.8646
EMA
1 2 3 4 5 Avg.
6.1598 5.2761 7.8021 4.7904 5.7531 5.9563
9.7091 8.7536 10.3592 7.9896 8.9342 9.1491
7.5826 6.9114 8.6429 5.8542 7.2745 7.2531
20.1917 19.3380 21.1273 18.5411 19.6972 19.7790
11.516 10.8749 9.3164 10.5967 11.2364 11.0051
22.8321 21.7127 20.4741 9.5937 21.9354 22.1414
B. Computational complexity issues
As the block based approach greatly reduces computational complexity when the input sequence is excessively large, the proposed schemes provide elegant means to remove noise from the EEG signal. Table I provides comparative account of various algorithms in terms of number of operations required. The computational complexity of TDBNLMS and FDBNLMS is similar to TDBLMS and FDBLMS except that some more computations are required for calculating variable step size. In the case of TDBNLMS, the normalized version of step size requires one division, L multiplications and accumulations (MACs) for the denominator part. By using a technique called distributive arithmetic, the denominator of normalized technique can be realized with zero multiplications.32 In our experiments in order to reduce this complexity, a block-based approach is used in which the input data are partitioned into blocks, and the maximum magnitude within each block is used to compute step size. Therefore, the computation of denominator requires only one MAC. III. SIMULATION RESULTS
To show that the proposed algorithms are really effective in clinical situations, the methods have been validated using
several EEG recordings with a wide variety of wave morphologies recorded using the Emotive EPOC headset33 which has 14 data-collecting electrodes and 2 reference electrodes. The electrodes are placed in roughly the international 10-20 system and are labeled as such.34 The headset transmits encrypted data wirelessly to a Windows-based machine; the wireless chip is proprietary and operates in the same frequency range as 802.11(2.4 GHz). Using this BCI, we have recorded brain signals with various artifacts from 5 subjects. The headset samples all channels at 128 samples/second, each of which is a 4-byte floating-point number corresponding to the voltage of a single electrode. The data rate of the EEG data streamed from the relay laptop to the mobile phone is 4 kbps per channel. In our simulation, we have recorded 200 000 samples. But due to space constraint to show high resolution signal, we have used first 1000 samples. In our experiments, we have implemented and tested adaptive filters with the three cases, i.e, (1). P = L = 10, (2). P = 5, L = 10, and (3). P = 10, L = 5. Among the three, the first case gives better performance in terms of signal to noise ratio (SNR) measurement (the results shown in this paper are for this case). For evaluating the performance of proposed filter structures, we have measured signalto-noise ratio improvement (SNRI), Excess Mean Square Error (EMSE), MSD, and Coherence (CHO) in ten experiments,
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TABLE III. Performance contrast of various ANCs for EEG signal enhancement.
Noise
Characteristics
LMS
NLMS
TD BLMS
FD BLMS
TD BNLMS
FD BNLMS
PLN
EMSE MSD CHO
−15.2858 0.0852 0.6210
−20.5372 0.0578 0.8842
−23.1546 0.0295 0.9425
−28.4315 0.0098 0.9813
−25.5496 0.0152 0.9673
−30.6431 0.0053 0.9875
EMG
EMSE MSD CHO
−18.6242 0.1164 0.6729
−23.7342 0.0852 0.8430
−26.6331 0.0645 0.8921
−31.4324 0.0326 0.9654
−28.0263 0.0429 0.9165
-33.3754 0.0295 0.9795
CSA
EMSE MSD CHO
−17.7639 0.0967 0.6462
−22.7537 0.0643 0.8636
−25.4185 0.0384 0.9372
−30.8564 0.0169 0.9684
−27.7565 0.0274 0.9527
−32.5631 0.0147 0.9857
RA
EMSE MSD CHO
−15.6793 0.0915 0.6436
−20.8540 0.0474 0.7932
−23.5975 0.0396 0.8563
−28.8164 0.0195 0.9725
−25.9647 0.0264 0.9146
−31.3659 0.0153 0.9864
EMA
EMSE MSD CHO
−16.3627 0.0984 0.6364
−21.6342 0.0685 0.8894
−24.9353 0.0427 0.9383
−29.8452 0.0256 0.9665
−26.0453 0.0315 0.9502
-31.7234 0.0175 0.9715
averaged, and compared with conventional LMS based ANC. For all the figures, the number of samples is taken on x-axis and amplitude on y-axis, unless stated. As the practical application of the proposed implementation is in biotelemetry, since the nature of channel noise is Gaussian, so to resemble channel noise in our experiments, we added a Gaussian noise with variance of 0.01. The choice of this value of variance has been performed after different trials so that the additional Gaussian noise does not determine the removal of useful information but only cancels envisaged artifacts. Such value is the optimal. However, for the case of the artwork, since we deal with EEG
signals, neurologists generally add Gaussian noise with their recording instrumentation to smooth final undesired noise. They do that empirically. As it is an adaptive system, the indicated value corresponds to the best one that produces the minimum error. Usually, with the sample amplitude as it is pointed out in the paper, acceptable values of variance range from 0.005 up to 0.02. Table II gives the SNRI contrast of various artifact eliminations. Table III gives the contrast of all algorithms in terms of EMSE, MSD, and CHO. In our experiments, we have considered a dataset of five EEG records: Record 1, Record 2,
FIG. 2. Typical brain signal enhancement results of PLN cancelation due to various ANCs: (a) EEG Signal with PLN, (b) a typical PLN, (c) LMS based ANC, (d) NLMS based ANC, (e) TDBLMS based ANC, (f) FDBLMS based ANC, (g) TDBNLMS based ANC, (h) FDBNLMS based ANC.
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These are recorded using the Emotive EPOC headset with a sampling frequency 128 samples/second. A random noise is added to the ECG signals to resemble channel noise while transmission. The input SNR for the above non-stationary noise is taken as 1.25 dB. B. Adaptive cancelation of PLN
Record 3, Record 4, and Record 5 to ensure the consistency of results. Various ANCs are implemented using LMS, NLMS, TDBLMS, FDBLMS, TDBNLMS, and FDBNLMS algorithms. Various experiments are performed to remove several artifacts from the recorded brain signals, these results are shown in Figs. 2–9, presented as follows.
This experiment demonstrates PLN cancelation. The input to the filter is EEG signal corrupted with PLN of frequency 50 Hz and sampled at 160 Hz recorded from a male person aged 41 (this signal is considered as Record 1). The reference signal is synthesized PLN; the output of the filter is recovered signal. The EMSE behavior of various ANCs is shown in Fig. 3. We have performed this experiment on five EEG records for ten times and averaged. Various performance measures like, SNRI, EMSE, MSD, CHO are tabulated in Tables II and III. Due to space constraint filtering results of record 1 are shown in this paper, it is shown in Fig. 2. In SNRI measurements, it is found that FDBNLMS algorithm gets SNRI of 22.9427 dB, FDBLMS gets 20.2964 dB, TDBNLMS gets 15.1640 dB, NLMS gets 14.7393 dB, TDBLMS gets 8.2756 dB, where as the conventional LMS algorithm improves to 7.4371 dB.
A. Noise generator
C. Adaptive cancelation of EMG
The desired signal d(n) shown in Fig. 1 is taken from noise generator. A synthetic PLN with 1 mV amplitude is generated for PLN cancelation; no harmonics are synthesized. In order to test the filtering capability in the non-stationary environment, we have considered real EMG, CSA, RA, and EMA noises.
The contaminated brain activity signal is applied as primary input to the adaptive filter of Fig. 1; reference signal is taken from our noise generator. This noise generator design synthesizes various artifacts which are in some way correlated with the power spectral distribution of noise component
FIG. 3. A typical EMSE behavior for the removal of PLN from brain signals.
FIG. 4. Typical brain signal enhancement results of EMG cancelation due to various ANCs: (a) EEG Signal with EMG, (b) a typical EMG artifact, (c) LMS based ANC, (d) NLMS based ANC, (e) TDBLMS based ANC, (f) FDBLMS based ANC, (g) TDBNLMS based ANC, (h) FDBNLMS based ANC.
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FIG. 5. Typical brain signal enhancement results of CSA cancelation due to various ANCs: (a) EEG Signal with CSA, (b) a typical CSA, (c) LMS based ANC, (d) NLMS based ANC, (e) TDBLMS based ANC, (f) FDBLMS based ANC, (g) TDBNLMS based ANC, (h) FDBNLMS based ANC.
present in the input signal. This noise generator has different types of artifacts which can be used as reference signals in enhancement process. The adaptive filter has an innate ability to change its coefficients, so that the reference signal made equivalent to noise component in the input signal. The simulation results for record 1 are plotted in Fig. 4. From the performance measure tabulated in Tables II and III, it is clear that NLMS based noise canceler performs better than other algorithms. In SNRI measurements, it is found that FDBNLMS algorithm gets SNRI of 21.1257 dB, FDBLMS gets 19.0728 dB, TDBNLMS gets 11.8920 dB, NLMS gets 9.7810 dB, TDBLMS gets 6.5351 dB, where as the conventional LMS algorithm improves to 5.2187 dB. D. Adaptive cancelation of CSA
physiological artifact in the EEG signal. In our experiments, we performed the cancelation of such artifact from brain activity. The output signals from various ANCs based on mean square approach are shown in Fig. 7. Various performance measuring characteristics are tabulated in Tables II and III. In SNRI measurements, it is found that FDBNLMS algorithm gets SNRI of 20.7543 dB, FDBLMS gets 17.1979 dB, TDBNLMS gets 12.6523 dB, NLMS gets 10.3511 dB, TDBLMS gets 5.7870 dB, where as the conventional LMS algorithm improves to 4.8476 dB. F. Adaptive cancelation of EMA
In this experiment, the noisy EEG signal is given to ANC structure shown in Fig. 1; the reference is taken from noise
During acquisition of EEG signal, cardiac signal contaminates the brain potential. This results in high amplitude cardiac activity in brain activity signal. For better analysis of EEG signal, we apply EEG with CSA to various ANCs designed based on mean square approach. The filtered signals are shown in Fig. 5; the EMSE curves are shown in Fig. 6. Various performance measuring characteristics are tabulated in Tables II and III. In SNRI measurements, it is found that FDBNLMS algorithm gets SNRI of 21.9853 dB, FDBLMS gets 18.7257 dB, TDBNLMS gets 10.8270 dB, NLMS gets 9.7995 dB, TDBLMS gets 6.5871 dB, where as the conventional LMS algorithm improves to 5.5218 dB. E. Adaptive cancelation of RA
Because of the patients breathing activity, the base line of the EEG signal wanders up and down, causes some
FIG. 6. A typical EMSE behavior for the removal of CSA from brain signals.
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FIG. 7. Typical brain signal enhancement results of RA cancelation due to various ANCs: (a) EEG Signal with RA, (b) a typical RA, (c) LMS based ANC, (d) NLMS based ANC, (e) TDBLMS based ANC, (f) FDBLMS based ANC, (g) TDBNLMS based ANC, (h) FDBNLMS based ANC.
generator. Noise free brain signals after the elimination of EMA are shown in Fig. 8; the EMSE curves are shown in Fig. 9. Various performance measuring characteristics are tabulated in Tables II and III. In SNRI measurements, it is
found that FDBNLMS algorithm gets SNRI of 22.8321 dB, FDBLMS gets 20.1917 dB, TDBNLMS gets 11.5160 dB, NLMS gets 9.7091 dB, TDBLMS gets 7.5826 dB, where as the conventional LMS algorithm improves to 6.1598 dB.
FIG. 8. Typical brain signal enhancement results of EMA cancelation due to various ANCs: (a) EEG Signal with EMA, (b) a typical EMA, (c) LMS based ANC, (d) NLMS based ANC, (e) TDBLMS based ANC, (f) FDBLMS based ANC, (g) TDBNLMS based ANC, (h) FDBNLMS based ANC.
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FIG. 9. A typical EMSE behavior for the removal of EMA from brain signals.
IV. CONCLUSION
In this paper, the process of artifact removal from EEG signals corrupted by various artifacts using block based adaptive filters in both time and frequency domains was presented. The various filter structures based on TDBLMS, FDBLMS, TDBNLMS, and FDBNLMS algorithms are developed for EEG noise cancelation. For this, the input and the desired response signals are properly chosen in such a way that the filter output is the best least squared estimate of the original EEG signal. The proposed treatment exploits the modifications in the weight update formula and thus pushes up the speed over the respective LMS based realizations. From the simulation results, it is clear that the tracking capability of these algorithms in presence of non-stationary noise environment is better. Our simulations, however, confirm that the SNRI of the block filters is better than that of LMS algorithm. Also, the computational complexity of frequency domain filters is less than that of their time domain implementations. Hence, these systems are well suited for biotelemetric brain data analysis. 1Atlas:
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