Neuromagnetic source imaging with FOCUSS: a recursive weighted minimum norm algorithm.

The paper describes a new algorithm for tomographic source reconstruction in neural electromagnetic inverse problems. Termed FOCUSS (FOCal Underdetermined System Solution), this algorithm combines the desired features of the two major approaches to electromagnetic inverse procedures. Like multiple current dipole modeling methods, FOCUSS produces high resolution solutions appropriate for the highly localized sources often encountered in electromagnetic imaging. Like linear estimation methods, FOCUSS allows current sources to assume arbitrary shapes and it preserves the generality and ease of application characteristic of this group of methods. It stands apart from standard signal processing techniques because, as an initialization-dependent algorithm, it accommodates the non-unique set of feasible solutions that arise from the neuroelectric source constraints. FOCUSS is based on recursive, weighted norm minimization. The consequence of the repeated weighting procedure is, in effect, to concentrate the solution in the minimal active regions that are essential for accurately reproducing the measurements. The FOCUSS algorithm is introduced and its properties are illustrated in the context of a number of simulations, first using exact measurements in 2- and 3-D problems, and then in the presence of noise and modeling errors. The results suggest that FOCUSS is a powerful algorithm with considerable utility for tomographic current estimation.