Probabilistic Enhancement of EEG Components Using Prior
Information of Component-Related Spatial Correlation
Hayato Maki, Tomoki Toda, Sakriani Sakti, Graham Neubig, and Satoshi Nakamura
Abstract— We propose a probabilistic scheme to enhance thetarget component of electroencephalogram (EEG) using a multichannel Wiener filter with time-variant spatial correlation matrices estimated using maximum a posteriori (MAP) estimation.

I. INTRODUCTION
Independent component analysis (ICA) is a widely usedmethod for improving EEG signal-to-noise ratios [1]. Itworks well under the assumption that the number of sources
is equal to or less than the number of sensors, which is questionable in the context of EEG. Sakanashi, et al [2] proposeda probabilistic audio separation scheme using a Wiener filter
in which time-variant spatial correlation matrices of eachcomponents are estimated using the maximum likelihood
criterion. We apply this scheme to enhancement of the target
EEG signal component, and improve its performance bysetting prior distributions to spatial correlation matrices andusing MAP criterion for parameter estimation.

III. MAXIMUM A POSTERIORI ESTIMATION OF
SPATIAL CORRELATION MATRICES
We assume a situation where features of the target component is known; e.g., the ERP of P300 component needs tobe enhanced as the target component in some applications.
Therefore, we can set the prior distributions of each Rk asp(R−1k |Ψk ) = W(Ψk , q),(3)where W is Wishart distribution. Ψk and q are hyper
parameters which are determined in advance using prerecorded EEG signals. We estimate parameters that maximize
following posterior probability using the EM algorithm,∏∏p(R|x, v, α) =p(x(n, f )|θ)p(R−1(4)k |Ψk )
n,fk

where R = {R1 , · · · , RK }. Each components’s time-variant
spatial correlation matrix is given as follows:
Rck (n, f ) = mk (n, f )vk (n, f )Rk .

(5)

where mk (n, f ) is the posterior probability.
II. OBSERVATION MODEL
Following previous work’s observation model [2], we denote the complex amplitude of an observation multi-channel
EEG signal in the time-frequency domain as x(n, f ) =[x(1) (n, f ), · · · , x(J) (n, f )]⊤ and that of its k-th component(1)(J)
as ck (n, f ) = [ck (n, f ), · · · , ck (n, f )]⊤ where n is
the index of a time frame, f is that of a frequency bin
and J is the number of EEG channels. We assume thatck (n, f )follows a multivariate complex Gaussian with a zeromean vector as follows:p(ck (n, f )) = N (ck ; 0, vk (n, f )Rk ),(1)

IV. ENHANCEMENT WITH WIENER FILTER
We construct a multi-channel Wiener filter and enhancethe target components [2],)−1(K∑Rck (n, f )x(n, f ). (6)ck (n, f ) = Rck (n, f )k=1

V. EXPERIMENTAL EVALUATION
A subject participated in an experiment of the oddballparadigm using a 27 channel EEG. By our proposed method,
the S/N ratio is improved (see Fig.1) and the accuracyof pattern recognition (200 standard stimuli v.s. 50 targetstimuli) was improved from 64% (raw) to 79% (proposed).

where vk (n, f ) is the degree of activeness of the k-th component in (n, f ) and Rk is a spatial correlation matrix thatrepresents the correlation between EEG channels. Therefore,
the likelihood of the observation signal is written asp(x|θ) =K∏∑

αk N (x(n, f ); 0, v(n, f )Rk ).

(2)

n,f k=1

where θ = {αk , vk (n, f ), Rk }K
k=1 , and αk is the probabilityof k-th component’s being active in each (n, f ).
H. Maki is a M. Eng. candidate at the Graduate School of Information
Science, Nara Institute of Science and Technology (NAIST), Japan, (email:maki.hayato.lt3@is.naist.jp). Tomoki Toda, Sakriani Sakti, GrahamNeubig, and Satoshi Nakamura are with NAIST. This work was supported
by JSPS KAKENHI Grant Number 24240032.

Fig. 1.

Raw signal (left) and after the proposed method (right)

R EFERENCES[1] A.Hyvarinen, J.Karhunen, and E.Oja. Independent component analysis. Vol. 46. John Wiley Sons, 2004.
[2] R.Sakanashi, et al. ”Comparison of superimposition and sparse models in blind source separation by multichannel Wiener filter.” Proc.
APSIPA, 2012