Improving the performance of linear inverse solutions by inverting the resolution matrix

This paper proposes a new strategy for improving the localization capabilities of linear inverse solutions, based on the relationship between the real solution and the estimated solution as described by the resolution matrix equation. Specifically, we present two alternatives based on either the partial or total inversion of the resolution matrix and applied them to the minimum norm solution, which is known for its poor performance in three-dimensional (3-D) localization problems. The minimum norm transformed inverse showed a clear improvement in 3-D localization. The strong dependence of localization errors with the eccentricity of the sources, characteristic of this solution, disappears after the proposed transformation. A similar effect is illustrated, using a realistic example where multiple generators at striate areas are active. While the original minimum norm incorrectly places the generators at extrastriate cortex, the transformed minimum norm localizes, for the example considered, the sources at their correct eccentricity with very low spatial blurring.