WO2012134260A2

WO2012134260A2 - Methodology of extracting brain erp signals from background noise

Info

Publication number: WO2012134260A2
Application number: PCT/MY2012/000040
Authority: WO
Inventors: Aamir SAEED MALIK; Yusoff MOHD ZUKI; Kamel NIDAL
Original assignee: Institute Of Technology Petronas Sdn Bhd
Priority date: 2011-02-28
Filing date: 2012-02-28
Publication date: 2012-10-04
Also published as: WO2012134260A3; MY152983A

Abstract

The present invention relates generally to methodology of extracting brain event related potential (ERP) signals from electroencephalogram (EEG) background noise using Generalized subspace-based algorithm.

Description

METHODOLOGY OF EXTRACTING BRAIN ERP SIGNALS FROM BACKGROUND NOISE

1. TECHNICAL FIELD OF THE INVENTION

2. BACKGROUND OF THE INVENTION

Event-related potential (ERP) is a term used to describe stereotyped electrophysiological response to an internal or external stimulus or any measured brain response that is directly the result of a thought or perception. Processes that may cause ERP involve memory, expectation, attention or changes in the mental state among others. While evoked potential (EP) is an electrical potential recorded from the nervous system of a human or other animals following presentation of a stimulus. There are three different types of non- invasive and relatively inexpensive EP tests used in clinical diagnosis namely the visual evoked potential (VEP) test, the brainstem auditory evoked potential (BAEP) and the somatosensory evoked potential (SSEP) tests. In clinical environments, the stated tests are primarily used by clinicians to objectively check the conduction of nerve signals (vision-, hearing-, or feel-triggered) that are transmitted to the brain and spinal cord. Normally, the nerve signals reaching the brain and spinal cord will produce waveforms with certain amplitudes and time delays, also known as latencies.

Generally, both ERP and EP can be measured by using a technique called electroencephalography (EEG). This is important in diagnosing some diseases or abnormalities possessed by patients. For example in VEP test, P100 components collected from EEG usually produce latencies very close to 100 ms for normal subjects. On the contrary, subjects with defective visual pathways will register prolonged P100 latencies (e.g., at 120 ms, 130 ms, etc.). Therefore, changes in the VEP amplitudes or latencies can be correlated to specific diseases or disorders possessed by patients. A study indicated that the P100 components registered higher waveform amplitudes in patients with "explosive behaviours" than those with normal behaviours. Some extensive studies also suggest that diseases such as diabetic retinopathy and multiple sclerosis affect the optic nerve and cause delays (i.e., increased latencies) in the signal conduction.

EEG usually reflects thousands of simultaneous on-going brain processes. The brain response to a single stimulus or event of interest is not usually visible in the EEG recording of a single trial. In order to view the brain response to a specific stimulation applied to a subject under study, multiple trials (i.e. 100 trials or more) must be conducted to cause random brain activity to be averaged out and hence to remain the relevant ERP. Estimating ERP or EP from the human brain is rather challenging as the signal-to-noise ratio (SNR) is generally very low. For example, EEG is a highly correlated type of noise that usually exists at higher level than VEP, with a typical SNR of -5 to -10 dB. VEP are conventionally extracted from the spontaneous brain activity by collecting a series of time-locked electroencephalogram (EEG) epochs and performing ensemble averaging (EA) on these samples to improve the SNR. However, the EA scheme requires a large VEP sample ranging from one hundred to two hundred different realizations. The recorded observations are then added together to obtain a cleaner waveform and approximating the desired VEP. Therefore even the use of EA technique does improve SNR, the longer recording time may cause discomfort and fatigue to the subject under study. Furthermore, multi-trial averaging contributes to loss of distinctive physiological information which may prove useful for thorough optical pathway conduction assessment, disease diagnosis and other fields of study such as psychology and pharmaceuticals. As such, an estimation scheme based on a single trial which minimizes the information loss and reduces ERP or EP recording time is highly desirable.

There are some VEP estimation techniques such as Subspace Regularization Method (SRM) proposed by Karjalainen et al, Third- Order Correlation (TOC)-based Filtering Approach proposed by Gharieb and Cichocki and Subspace-based Dynamical Estimation Method (SDEM) proposed by Georgiadis et al. The main emphasis of all the techniques listed above is on the accurate detection of the VEP peak latencies, instead of the accurate estimation of the amplitudes. In addition, extensive experiments involving simulated and real data showed that failure rate and percentage errors produced by the said techniques are still relatively high. The present invention overcomes the above shortcomings by providing a methodology of extracting brain ERP signal from background noise by using subspace approach with pre-whitening for measurement of latencies in ERP. The developed subspace based algorithm uses linear estimator to estimate the clean ERP signal by minimizing signal distortion while maintaining the residual noise energy below a given threshold. The generalized subspace is then used to decompose the space into a signal subspace and noise subspace. Enhancement is performed by removing the noise subspace and estimating the clean signal from the remaining signal subspace.

3. SUMMARY OF THE INVENTION

Accordingly, it is the primary aim of the present invention to provide a methodology of extracting brain ERP signals from background noise by using a subspace approach with pre-whitening for measurements of latencies in ERP.

It is yet another objective of the present invention to provide a methodology of extracting brain ERP signals from background noise by conducting only single or few trials. Yet a further object of the present invention is to provide a methodology of extracting brain ERP signals from background noise wherein fatigue experienced by patients due to long acquisition time is reduced. Yet a further object of the present invention is to provide a methodology of extracting brain ERP signals from background noise wherein artifacts introduced by fatigue is reduced.

It is a further object of the present invention to provide a methodology of extracting brain ERP signals from background noise that is able to extract ERP signal at low SNR values.

It is yet another objective of the present invention to provide a methodology of extracting brain ERP signals from background noise that is non-invasive.

Other further objects of the invention will become apparent with an understanding of the following detailed description of the invention or upon employment of the invention in practice. These and other objects are achieved by the present invention, which in its preferred embodiment provides,

A methodology of extracting brain event-related potential (ERP) signals from electroencephalogram (EEG) signal background noise, comprising of the following steps: i. performing acquisition of brain signals; ii. extracting ERP signals; characterized in that the extraction of ERP signals is done by the following sub-steps: ia. developing generalized subspace algorithm by minimizing the distortion in the ERP signal while maintaining the level of the EEG noise below a given threshold; ib. enhancing the level of the extracted ERP signals in ia by implementing said generalized subspace algorithm. 4. BRIEF DESCRIPTION OF THE DRAWINGS

Other aspects of the present invention and their advantages will be discerned after studying the Detailed Description in conjunction with the accompanying drawings in which: FIG. 1 shows a flow chart outlining the general steps of developing generalized subspace algorithm of extracting brain ERP signal from background noise with explicit pre-whitening.

FIG. 2 shows a flow chart outlining the general steps of developing generalized subspace algorithm of extracting brain ERP signal from background noise with implicit pre-whitening.

FIG. 3 shows a flow chart outlining the general steps of implementing generalized subspace algorithm of extracting brain ERP signal from background noise.

5. DETAILED DESCRIPTION OF THE DRAWINGS In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the invention. However, it will be understood by those or ordinary skill in the art that the invention may be practiced without these specific details. In other instances, well known methods, procedures and/or components have not been described in details so as not to obscure the invention.

The invention will be more clearly understood from the following description of the embodiments thereof, given by way of example only with reference to the accompanying drawings which are not drawn to scale. In developing a mathematical expression for extracting a ERP signal, two subspace algorithms can be used as generalized subspace approach (GSA), which are explicit pre-whitening (GSAE) and implicit pre-whitening (GSAI).

Development of GSA with Explicit Pre-whitening (GSAE) Referring now to FIG. 1, there is shown a flow chart outlining the general steps of developing generalized subspace algorithm of extracting brain ERP signal from background noise with explicit pre- whitening. In developing of GSA with explicit pre-whitening (GSAE), the following model is defined. y(k) = x(k) + n(k) (1) where, the lowercase k is the discrete time index; y(k) e R^M is the M- dimensional vector of the corrupted ERP; x(k) e R^M is the M- dimensional vector of the clean ERP signal; n(k) e R^M is the M- dimensional vector of the post-stimulation EEG noise, assumed to be uncorrected with x(k). Next, H( c) eR^MxM is defined as the MxM- dimensional matrix of the ERP linear-time-domain constraint (TDC) estimator. Further, x(k) e R^M is defined as the M-dimensional vector of

)

the estimated ERP signal. Afterwards, any vectors or matrices that appear without a time index should be visualized as having the ks as their time indexes.

In order to satisfy the pre-whitening requirement, the estimated ERP signal ( x ) is related to H as follows: x = R_n . H . R_n ^ly (2) where R_n is the correlation matrix of the post-stimulation EEG noise. R_n can be computed from brain EEG during which no stimulation is applied. The corrupted ERP signal (y) is first whitened by the R_n ^'x term. The whitened data are modified further by H. The modified signal is later de-whitened by the R_N term.

The estimated ERP signal ( x ) will never be exactly equal to the original (clean) ERP signal (x); errors will inevitably be produced in the ERP signal. Basically, the system equation in (2) is to minimize a specified error criterion. The error signal (ε) obtained by this estimation is as follows: f = x - x = [R_H HR^~x - l)x + R_NHR^~ n

= e_x + e_n , e_x = {R_NHR ^~ - l)x and e„ = R_NHR ^~ n (3) where ί represents identity matrix, ε_χ represents the ERP distortion and ε_η represents the residual EEG noise. The energies of the ERP

_2

signal distortion t_x can be calculated as the expectation of the outer product of £_Λ by itself; that is, e = tr( .A })= tr H*,;¹ -I)R_x{R_nHR_n -if ) . ^' (4) where R_X is the correlation matrix of the ERP signal. Similarly, the energies of the residual noise ( e² ) can be calculated as follows: = })= )*„ ) (5)

Now, the total residual energies can be expressed as Both the said unwanted energies shall be minimized so that a minimal error signal is obtained. However, when the ERP signal distortion is at its lowest, the EEG noise residuals will be at its highest; on the other hand, if noise is fully minimized, distortion will be at its greatest. Therefore, a proper balance shall be identified so that the noise residuals can be reasonably minimized without introducing significant distortion to the processed signal.

A linear estimator (H) is designed to minimize the ERP signal distortion over all linear filters by maintaining the residual noise within a permissible level. Mathematically, the optimum linear estimator (H_opt) with time-domain constraints on the residual noise is formulated as follows:

H_opt subject to: e ² < Mo ² (7)

where M is the dimension of the noisy vector space and σ² is a positive constant noise threshold level. The σ² in (7) dictates the amount of the residual noise allowed to remain in the linear estimator. Next, the Lagrangian function in association with the "Kuhn-Tucker necessary conditions for constrained minimization" are applied to (7) to obtain an optimal H. The formed Lagrangian function can be expressed as: L(H, n) = tl + μ(£ ^■Mo ² ) (8)

It follows that the filter matrix H is a stationary feasible point if it satisfies the following gradient equation VHL(H, μ) = 0:

— -—— = ί, + (C„ - Mr )] = 0

3H dH ^x " ₍₉₎

^ R_nH{R-^yR_x + μΓ) = R_x Subsequently, (9) can be solved to yield the required H:

where, μ is the Lagrange multiplier which has to be set to a proper value. The higher value of μ eliminates more post-stimulation EEG noise residuals at the expense of higher distortion in the recovered ERP.

Other Kuhn-Tucker necessary conditions to be fulfilled are: μ(£_η ² -Μχ²) = 0 (11) for μ≥0 (12) The values for μ and σ ² satisfying (11) and (12) need to be determined. Equation (11) can be simplified to yield

?² = σ² (13) The following expression for σ² is obtained by equating (13) with (5): n = Μσ² = tv({R_nHR_n-' )R_n (R_nHR_n ^'l )^T )

(14) => σ² =→r((R_nHR ^] )R_n (R_nHR- )

Equation (14) is more meaningful if a relationship between a² and μ can be established. This is achieved by replacing H computed in (10) into (14).

One issue that arises from (15) is whether to first specify the permissible level of residual noise σ² , or the Lagrange multiplier μ.

The first approach is to specify a² in (15) and calculate μ from it. On the other hand, μ can be carefully chosen so that a² can be calculated. Therefore, μ which satisfies (15) also satisfies (11) and (12). Hence, μ must also be the Lagrange multiplier for the time-domain-constrained (TDC) optimization problem of (7).

With reference to (10), generalized eigenvalue decomposition is to be performed on R_x and R_n. The said eigendecomposition of the symmetrical matrix R_a = R^~ R_X leads to the following:

R_aV = VA <→R_a = VA V -1 By substituting R_A = R R_X into (16):

R_XV = R_nVA (16A) where R_x = V^'T A V^~] (16B)

V^TR_NV = A_N ^ R_N = V-^TA_N V-¹ <-> R_N = V ^ V^T (17) where A and V are, respectively, the eigenvalue and non-unitary eigenvector matrices of R_A . By putting (16) into (10), we can write H as

HasAE = VA V {VA ν^~ + μΐΓ = VA(A + μΙ)^~ V

At Λ (18)

= VGV-' where G = A(A + μϊ) where, G is known as a gain matrix. Based on (2) and (18), the estimated ERP can be expressed

Xas E = · H_GSAE . Rjy = R_nVGV^~lR^~l . y By using (17), we can express (19) as

CSAE = V^~T A V^~lVGV^~lVA^~lV^T .

(20)

= V-^TGV^T » y, G = A(A + J)

The corrupted ERP signal y in (20) is decorrelated by the forward matrix V^T . Then, the transformed signal is modified by the signal subspace gain matrix G. Next, the modified signal is retransformed back into the original form by the inverse matrix K^~r to obtain the desired signal.

In formulation of signal detection problem, Akaike Information Criteria (AIC) approach is adapted to handle the signal and noise subspace separation problem. The extended AIC is given by following equation:

AIC(£) = arg min 2k(2Q - k) (21)

where g(k) is the geometric mean of the smallest Q-P eigenvalues expressed as g(k) = Π l ^~k) (22) where Z, is the eigenvalues of the sample covariance matrix and a(k) is the arithmetic mean of the smallest Q-P eigenvalues given by

Q

a(k) = ∑ (23)

Q - k j=k+l

The desired number of signals is determined as the value of k e [0, Q-1] for which the AIC is minimized. With the use of Eqs. (22) and (23), the AIC in Eq. (21) can now be written as

Further, modification is required as follows: i. The eigenvalues lj is to be replaced by the eigenvalues j of the Generalized Subspace Approach (GSA).

ii. The N which represents the number of observations or

snapshots is treated as unity (i.e., N = 1).

Thus, equation (24) can be simplified as follows:

By using AIC, dimension of eigenvalues V is estimated to produce reduced dimension of eigenvectors Vu and reduced dimension of eigenvalues Ak from (18):

^Λ H^ί enhanced = V ^v k^'TG k V^r k^T -1

where G_k = A_k (A_k + μΐ) (26)

Hence, estimated ERP x i_s obtained by multiplying enhanced ERP estimator HenUanced with corrupted ERP y:

* = ^H enhanced ' = ^ ' ^G 'k * ^ (₂7)

The estimation of Lagrange multiplier μ is carried out by adjusting said Lagrange multiplier μ from 0 to 24 for every SNR level. For example, at 0 dB, μ was initially set to 0 and the algorithm was run for 500 times. The failure rate and average errors were then noted. Next, μ was then changed to 1 and the algorithm was run again for another 500 times. The failure rate and average errors were again properly recorded. Still at 0 dB, the whole process was repeated for μ = 2 to μ = 24. Also, for the remaining SNRs from -1 down to -11 dB, the same stated procedures were repeated. Eventually for any SNR, the μ that resulted in the lowest failure rate and lowest average errors was regarded as the best approximated Lagrange multiplier. Table 1 below summarizes the best values of μ for the given range of SNRs. μ = 2 was found to be optimal in detecting the P100. Therefore, in determination of real patient data, μ=2 is chosen and is fixed by using ensemble averaging (EA) as baseline. If the SNR value can be eventually determined from real data, the value of μ can be adaptive.

Table 1 The best approximated Lagrange multiplier μ for the pertinent peaks across the SNR ranging from 0 to -11 dB.

Development of GSA with Implicit Pre-whitening (GSAI) Referring now to FIG. 2, there is shown a flow chart outlining the general steps of developing generalized subspace algorithm of extracting brain ERP signal from background noise with implicit pre- whitening.

In developing of GSA with implicit pre-whitening (GSAI), following model is defined.

y = x + n (28) where, y e R is the M-dimensional vector of the corrupted ERP; x e R^M is the M-dimensional vector of the clean ERP signal; n e R^M is the M-dimensional vector of the post-stimulation EEG noise, assumed to be uncorrelated with x. Next, HeR^MxM is defined as the MxM- dimensional matrix of the ERP linear-time-domain constraint (TDC) estimator. Further, x e R^M is defined as the M-dimensional vector of the estimated ERP signal.

In order to satisfy the implicit pre-whitening requirement, the estimated ERP signal ( x ) is related to H as follows: x = H . y (29)

The estimated ERP signal ( x ) will never be exactly equal to the original (clean) ERP signal (x); errors will inevitably be produced in the ERP signal. Basically, the system equation in (29) is to minimize a specified error criterion. The error signal (ε obtained by this estimation is as follows:

€ = x - x = (H - l )x + Hit

(30)

- ^{+ e} _n > t_x = (# - /) and e„ = Hn where ε_χ represents the ERP distortion and ε_η represents the residual EEG noise. The energies of the ERP signal distortion _x can be calculated as the expectation of the outer product of by itself; that is, ?_χ = r(E{e_xe_x ^T })= tr((H - I)R_x (H - I)^T ) (31) where R_x is the corellation matrix of the ERP signal. Similarly, the energies of the residual noise ( e„² ) can be calculated as follows: 2 = {½} ^(# ) (32)

Now, the total residual energies can be expressed as

2 = e_x ² + ] (33)

Both the said unwanted energies shall be minimized so that a minimal error signal is obtained. However, when the ERP signal distortion is at its lowest, the EEG noise residuals will be at its highest; on the other hand, if noise is fully minimized, distortion will be at its greatest. Therefore, a proper balance shall be identified so that the noise residuals can be reasonably minimized without introducing significant distortion to the processed signal.

A linear estimator (H) is designed to minimize the ERP signal distortion over all linear filters by maintaining the residual noise within a permissible level. Mathematically, the optimum linear estimator (H₀pt) with time-domain constraints on the residual noise is formulated as follows:

H_opt = min t subject to: < Ma¹ (34) H where M is the dimension of the noisy vector space and σ² is a positive constant noise threshold level. The a ² in (34) dictates the amount of the residual noise allowed to remain in the linear estimator. Next, the Lagrangian function in association with the "Kuhn-Tucker necessary conditions for constrained minimization" are applied to (34) to obtain an optimal H. The formed Lagrangian function can be expressed as:

L(H, ii) = e_x ² + μ(€_η ² - Ma ¹ ) (35)

It follows that the filter matrix H is a stationary feasible point if it satisfies the following gradient equation VHL(H, μ) = 0: dL(H^) d _{2 2} 2

= [e + u(e„ - Ma )] = 0

dH dH ^x " (36) > H{R_x + R_n ) = R_x

Subsequently, (36) can be solved to yield the required H_opt:

^Ηο_Ρ1 ^{= Κ Κ}* ^{+ μΚ}« ⁾ <³⁷) where, μ is the Lagrange multiplier which has to be set to a proper value. The higher value of μ eliminates more post-stimulation EEG noise residuals at the expense of higher distortion in the recovered ERP. Other Kuhn-Tucker necessary conditions to be fulfilled are:

μ(?² - σ²) = 0 (38) for μ > 0 (39)

The values for μ and a² satisfying (28) and (39) need to be determined. Equation (38) can be simplified to yield

The following expression for a² is obtained by equating (40) with (32):

n² = M ² = tr(HR_nH^T )

Equation (41) is more meaningful if a relationship between σ² and μ can be established. This is achieved by replacing H computed in (37) into (41).

— ¹ Φ,'(«, + Λ )^'!ί,) (42)

One issue that arises from (42) is whether to first specify the permissible level of residual noise a² , or the Lagrange multiplier μ. The first approach is to specify σ² in (42) and calculate μ from it. On the other hand, μ can be carefully chosen so that a² can be calculated. Therefore, μ which satisfies (42) also satisfies (38) and (39). Hence, μ must also be the Lagrange multiplier for the time-domain-constrained (TDC) optimization problem of (34).

With reference to (37), generalized eigenvalue decomposition is to be performed on R_x and R„and is given by the following:

R_xV = R_nVA (43)

Where A and V are, respectively, the generalized eigenvalue and generalized eigenvector matrices of R_x and R_n.

In addition to Equation (43), if there are two symmetrical matrices R_x and R_n then the generalized eigendecomposition enables R_x and R_n to be simultaneously diagonalized satisfying fully the following equations:

V^TR_XV = A_X = A ₍₄₄₎ v^T y = A_n = i ₍₄₅₎

It is crucial to note that from Equations (43), (44) and (45) that the generalized eigendecomposition of the two symmetrical matrices R and R_n results in non-unitary eigenvectors V (i.e., VW≠ WV≠ I; V-^T≠ V; V-¹≠ V¹). Equations (44) and (45) can be rearranged, respectively, as

R_x = V ^TA V ^l (46)

R_n = V^'rIV^~l (47) An optimal estimator HGSAI based on the generalized eigendecomposition of (R_X, R_N) can then be obtained by applying Equations (46) and (47) to Equation (37):

H_GSAI = V-^TA V- (V-^TA V^'1 + μν^~τΐν-¹ )^"'

= V^'TA V- (ν-^τ(Λ + μΙ)ν^~ι Υ

= V-^TA V^~ (v^+[ (Λ + μΐγ V^+T )

= ν-^τΛ(Λ + μΙ)-^ιν^+Γ (48) = V^'TGV^T where G = Λ{Λ + μΙ)^~χ

Based on Equation (48), the estimated ERP in Equation (29) is calculated as

— V^~r GV^T · y where G = Λ(Λ + μΙ)^~] The corrupted ERP signal y in (49) is decorrelated by the forward matrix v^T . Then, the transformed signal is modified by the signal subspace gain matrix G. Next, the modified signal is retransformed back into the original form by the inverse matrix v^~T to obtain the desired signal.

In formulation of signal detection problem, Akaike Information Criteria (AIC) approach is adapted to handle the signal and noise subspace separation problem. The extended AIC is given by following equation: AIC(£) = arg min - 2(Q - k)N + 2k(2Q - k) (21)

where g(k) is the geometric mean of the smallest Q-P eigenvalues j

expressed as g(k) = Π l) (22) j=k+\ where lj is the eigenvalues of the sample covariance matrix and a(k) is the arithmetic mean of the smallest Q-P eigenvalues given by

1

Q

Π i ^{Q ~ ^k)

j = k + l j

AIC(£) = -2(g - /t)N ln + 2k(2Q - k) (24)

Q

∑

j = k + \ j

Further, modification is required as follows: i. The eigenvalues lj is to be replaced by the eigenvalues λ] of the Generalized Subspace Approach (GSA). ii. The JV which represents the number of observations or snapshots is treated as unity (i.e., N - 1).

Thus, equation (24) can be simplified as follows: AlC(Jfc) - 2 2k(2Q - k) (25)

By using AIC, dimension of eigenvalues V is estimated to produce reduced dimension of eigenvectors Va and reduced dimension of eigenvalues Ad from (48):

¹ H¹ enhanced = V ^r d^'TG d V T

r d where G_d = Λ_Λ (A_d + μΐ) (50)

Hence, estimated ERP x i_s obtained by multiplying enhanced ERP estimator Henhanced with corrupted ERP y:

X = Henhanced ' =

(₅₁)

In this case, the Lagrange multiplier, μ=2 is used same as the explicit pre-whitening algorithm.

Referring now to FIG. 3, there is shown a flow chart outlining the general steps of implementing generalized subspace algorithm of extracting brain ERP signal from background noise. The said methodology comprises of eight steps which are indicated by eight individual blocks as shown in FIG. 3. From the said flow chart, it can be seen that the first step is recording pre-stimulation EEG, e and corrupted ERP, y as indicated by the first block of FIG. 3. This is followed by computing the correlation matrix of the corrupted ERP, R_y and estimating the correlation matrix of post-stimulation EEG, R_n using correlation matrix of pre-stimulation EEG R_e. Then the correlation matrix of the ERP signal is estimated as a difference between correlation matrix of corrupted ERP, R_y and correlation matrix of post-stimulation EEF, R_n as indicated by the fourth block. The fifth block shows the step of performing Generalized eigendecomposition of R_x and R_n on said ERP and EEG covariance matrices. In the sixth step, the dimension of significant eigenvalues (subspace dimension) is obtained by using of Akaike Information Criteria (AIC) approach and the obtained Lagrange multiplier (μ = 2) is utilized empirically. This is followed by the seventh step whereby the enhanced estimator, Hmhanced is computed and finally the enhanced estimate of ERP, x is calculated.

Hence, the developed method has incorporated optimization scheme with subspace filtering through the implementation of a linear estimation of the clean signal. This powerful combination between optimization and subspace significantly improves the performance of the proposed method in terms of lower average error and failure rate.

While the preferred embodiment of the present invention and their advantages have been disclosed in the above Detailed Description, the invention is not limited thereto but only by the scope of the appended claim.

Claims

WHAT IS CLAIM IS:

A methodology of extracting brain event-related potential (ERP) signals from electroencephalogram (EEG) signal background noise, comprising of the following steps: i. performing acquisition of brain signals; ii. extracting ERP signals; characterized in that the extraction of ERP signals is done by the following sub-steps: ia. developing generalized subspace algorithm by minimizing the distortion in the ERP signal while maintaining the level of the EEG noise below a given threshold; ib. enhancing the level of the extracted ERP signals in ia by implementing said generalized subspace algorithm.

2. A methodology of extracting brai ERP signals from electroencephalogram (EEG) background noise as claimed in Claim 1, wherein said developing generalized subspace algorithm is done using the following steps: i. defining a model corrupted ERP, y as a sum of clean ERP, x and post-stimulation EEG, n; ii. introducing ERP estimator matrix, H; iii. introducing estimated ERP, x■ iv- relating the said estimated ERP, ^x as multiplication of estimator, H and corrupted ERP, y; v. introducing error signal, £ as summation of ERP distortion, e_x and residual EEG noise, ε„; vi. optimizing or minimizing ERP estimator, H by

_2

minimizing ERP distortion energy, e_x while maintaining residual EEG noise energy, 1_n ² below a certain threshold value; vii. forming a Lagrangian function, L from constrained inequality and obtaining a gradient equation,

VHL(H, μ) = 0 to attain optimized ERP estimator H_opt, viii. applying generalized eigendecompositin on desired ERP correlation matrix, R_x and post-stimulation EEG noise correlation matrix, R_n to produce common eigenvector matrix, V and common eigenvalue matrix, A; ix. replacing R_x and R_n in ERP estimator, H_opt with eigenvectors, V and eigenvalues, A to obtain enhanced ERP estimator, Henhanced; x. estimating dimension of eigenvalues V using Akaike Information Criteria (AIC) to produce reduced dimension of eigenvectors Vd and reduced dimension of eigenvalues Ad,' xi. obtaining estimated ERP x by multiplying enhanced ERP estimator Hmhance with corrupted ERP y. A methodology of extracting brain ERP signals from electroencephalogram (EEG) background noise as claimed in Claim 1, wherein said implementing of said generalized subspace algorithm is done using the following steps; i. recording pre-stimulation EEG, e and corrupted ERP, y; ii. computing the corrupted ERP correlation matrix, R_y; iii. estimating the correlation matrix of post-stimulation EEG, R„ using correlation matrix of pre-stimulation EEG R_e, iv. estimating correlation matrix of ERP, R_x as a difference between correlation matrix of corrupted ERP, R_y and correlation matrix of post-stimulation EEF, R_n; v. performing Generalized eigendecomposition of R_x and

vi. obtaining dimension of significant eigenvalues (subspace dimension) using Akaike Information Criteria (AIC) approach and utilizing the obtained Lagrange multiplier (μ = 2) empirically; vii. computing enhanced estimator, H_enh nced; viii. calculating the enhanced estimate of ERP, x .

A methodology of extracting brain ERP signals from electroencephalogram (EEG) signal background noise as claimed in Claim 1 wherein said ERP signal can be from visual, audio, touch or any other brain stimulation.

A methodology of extracting brain ERP signals from electroencephalogram (EEG) signal background noise as claimed in Claim 1 wherein said ERP signals are obtained only using single trial (acquisition only done once).

A methodology of extracting brain ERP signals from electroencephalogram (EEG) signal background noise as claimed in Claim 1 wherein said ERP signals are obtained using a few trials by adding ensemble averaging method. A methodology of extracting brain ERP signals from electroencephalogram (EEG) signal background noise as claimed in Claim 1 or Claim 2 wherein pre-whitening of the corrupted ERP signal is performed during said developing of generalized subspace algorithm.

A methodology of extracting brain ERP signals from electroencephalogram (EEG) signal background noise as claimed in Claim 1 or Claim 2 wherein said step of developing generalized subspace algorithm is done using explicit pre- whitening.

A methodology of extracting brain ERP signals from electroencephalogram (EEG) signal background noise as claimed in Claim 1 or Claim 2 wherein said step of developing generalized subspace algorithm is done using implicit pre- whitening.