Informed spatial basis functions in minimum norm solutions for the electromagnetic source localisation problem.

Linear inverse Solutions have been applied extensively to solve the bioelectromagnetic inverse problem. In contrast to discrete dipole models, linear inverse solutions do not require any assumptions about the number of active sources and lead to a fully 3D representation of the electrical activity of the brain. However, the problem is underdetermincd: there are many more parameters to estimate (relative to the number of dipole locations considered) than data available (relative to the number of electrodes). In order to ensure the uniqueness of the solution, existing linear methods generally apply constraints on the solution, for example: minimum 2-norm, maximum smoothness [1], optimal resolution [2], etc. These methods provide solutions with relatively poor spatial resolution because they neglect, wholly or in part, anatomical Information relevant to the real source distribution. Our method aims to model the spatial source distribution by using a sei of basis functions. By appropriately defining these basis functions, we are able to include a priori Information about the sources and our Solutions will de facto belong to the subspace spanned by these basis functions. The priors enter äs constraints on the covariance structure of the source power (over space), and are used to motivate the selection of a spatial basis set that maximises the Information between the sources and their projection on that set. The orientation of each dipole is fixed and orthogonal to the cortical sheet, and therefore only the amplitude of the sources remains unknown. In a second step, we solve for the source distribution using a "classical" minimum norm method. Other methods could also be applied äs the informed basis functions are generated before the computation of the solution. Here we lest our method using a realistic head model and noiseless instantaneous simulated data.