The Compressible Estimate (CE) of MEG Current Sources

Abstract

Magnetoencephalography (MEG) non-invasively detects weak extracranial magnetic fields during tasks using super-conducting quantum interference devices (SQUIDs). The MEG inverse problem is to quantitatively model the underlying neuronal current sources by estimating their locations and orientations using MEG measurements. Many of the methods involve explicit preferences toward either spatially focal or diffused estimates of neuronal currents. However, considering a scenario that both focal and distributed current sources are simultaneously presented in the measurement, neither focal nor diffused bias is appropriate to reveal the underlying current sources. To address this challenge, we propose the Compressible Estimate (CE) based on the hypothesis that the current sources are sparse after a spatial transformation. CE promotes the compressibility of current sources by minimizing the ℓ₁-norm of transformed estimated current sources and avoids overly diffused source estimates by minimizing the ℓ₁-norm of estimated current sources. In this study we select the Laplacian and spherical wavelet as the spatial transformation. As demonstrated by the simulations and in vivo somatosensory and auditory experiments, CE provides the improved accuracy of the source localization involving both spatially focal and diffused neuronal currents.