Local Basis Expansions for MEG Source Localization

We discuss the use of local basis expansions (LBEX) for solving linear inverse problems with continuous source spaces. The LBEX method is a generalisation, to the linear inverse problem, of the multitaper technique for spectral analysis. The multitaper technique employs Slepian sequences, that are maximally concentrated in the frequency domain. The analog for LBEX are combinations of lead fields which are spatially concentrated in the source space. The method interpolates the minimum norm (MN) and Backus-Gilbert (BG) techniques, and is related to SOPHIA and beamspace methods in the context of MEG inverse problems. The technique is quite general, and applications include: localization of spontaneous activity, simultaneous localization in source space and temporal frequency, as well as semi-parametric localization of focal activity. Here we present some specific applications to MEG.