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In magnetoencephalography, linear minimum norm inverse methods are commonlyemployed when a solution with minimal a priori assumptions is desirable. Thesemethods typically produce spatially extended inverse solutions, even when thegenerating source is focal. Various reasons have been proposed for this effect,including intrisic properties of the minimum norm solution, effects ofregularization, noise, and limitations of the sensor array. In this work, weexpress the lead field in terms of the magnetostatic multipole expansion anddevelop the minimum-norm inverse in the multipole domain. We demonstrate theclose relationship between numerical regularization and explicit suppression ofspatial frequencies of the magnetic field. We show that the spatial samplingcapabilities of the sensor array and regularization together determine theresolution of the inverse solution. For the purposes of stabilizing the inverseestimate, we propose the multipole transformation of the lead field as analternative or complementary means to purely numerical regularization.

The effect of spatial sampling on the resolution of the magnetostatic inverse problem