Equivalent Dipole Source Imaging of Brain Electric Activity by Means of Parametric Projection Filter

Abstract

In the present study, spatial filters for inverse estimation of an equivalent dipole layer from the scalp-recorded potentials have been explored for their suitability in achieving high-resolution electroencephalogram (EEG) imaging. The performance of the parametric projection filter (PPF), which we propose to use for high-resolution EEG imaging, has been evaluated by computer simulations in the presence of a priori information on noise. An inhomogeneous three-concentric-sphere head model was used in the present simulation study to represent the head volume conductor. An equivalent dipole layer was used to model brain electric sources and estimated from the scalp potentials. Various noise conditions were simulated and the parametric projection filter was compared with standard regularization procedures such as the truncated singular value decomposition (TSVD) and the Tikhonov regularization (TKNV). The present simulation results suggest that the proposed method performs better than that of commonly used inverse regularization techniques, such as the general inverse using the TSVD and the TKNV, when the correlation between the original source distribution and the noise distribution is low, and performs similarly when the correlation is high. A method for determining the optimum regularization parameter, which can be applied to parametric inverse techniques, has also been developed.

Signal and Noise Covariance Estimation Based on ICA for High-Resolution Cortical Dipole Imaging

“…In these cases, our proposed method can demonstrate the behavior of individual sources using equivalent dipole distribution. We confirmed that several dipole sources could be represented by the PPFbased inverse filters [15]- [17] and the PWF-based inverse filter [21].…”

“…In actual situation, cortical sources may have a strong tangential component. The brain electrical activity caused by the tangential dipole sources could also be represented with the strength distribution of radial dipoles [15]. When some dipole sources simultaneously exist in the brain, the distributions caused by each source may be overlapped on the scalp map.…”

“…The determination of the value of parameter γ is left to the subjective judgment of the user. We have developed a criterion that estimates the optimum parameter using iterative calculation for restoration [15]. The criterion estimates the parameter that minimizes the approximated error between the original and estimated source signals without knowing the original source distribution.…”

“…The cortical dipole imaging requires solving an inverse problem described by the transfer function from the scalp potentials to the dipole layer. We have developed an inverse procedure for cortical dipole source imaging using a parametric projection filter (PPF) which enables estimation of inverse solutions in the presence of noise information [15]- [17]. Information related to noise distribution, as defined by the covariance matrix, was assumed to be known.…”

Electrophysiological Neuroimaging

“…The parametric projection filter (PPF), satisfying Eq. (7.26), is derived by (Oja and Ogawa, 1986;Ogawa and Oja, 1987;Hori and He, 2001) 5ppF = A^(A4^ + Ae)+ (7.27) Note, the PPF is a special case of the PWF, when R -I in Eq. (7.23).…”