On the Inverse EEG Problem for a 1D Current Distribution

الملخص EN

Albanese and Monk (2006) have shown that, it is impossible to recover the support of a three-dimensional current distribution within a conducting medium from the knowledge of the electric potential outside the conductor.

On the other hand, it is possible to obtain the support of a current which lives in a subspace of dimension lower than three.

In the present work, we actually demonstrate this possibility by assuming a one-dimensional current distribution supported on a small line segment having arbitrary location and orientation within a uniform spherical conductor.

The immediate representation of this problem refers to the inverse problem of electroencephalography (EEG) with a linear current distribution and the spherical model of the brain-head system.

It is shown that the support is identified through the solution of a nonlinear algebraic system which is investigated thoroughly.

Numerical tests show that this system has exactly one real solution.

Exact solutions are analytically obtained for a couple of special cases.