NEUROMAGNETIC SOURCE IMAGING WITH FOCUSS - A RECURSIVE WEIGHTED MINIMUM NORM ALGORITHM

The paper describes a new algorithm for tomographic source reconstruct ion in neural electromagnetic inverse problems. Termed FOCUSS (FOCal U nderdetermined System Solution), this algorithm combines the desired f eatures of the two major approaches to electromagnetic inverse procedu res. Like multiple current dipole modeling methods, FOCUSS produces hi gh resolution solutions appropriate for the highly localized sources o ften encountered in electromagnetic imaging. Like linear estimation me thods, FOCUSS allows current sources to assume arbitrary shapes and it preserves the generality and ease of application characteristic of th is group of methods. It stands apart from standard signal processing t echniques because, as an initialization-dependent algorithm, it accomm odates the non-unique set of feasible solutions that arise from the ne uroelectric source constraints. FOCUSS is based on recursive, weighted norm minimization. The consequence of the repeated weighting procedur e is, in effect, to concentrate the solution in the minimal active reg ions that are essential for accurately reproducing the measurements. T he FOCUSS algorithm is introduced and its properties are illustrated i n the context of a number of simulations, first using exact measuremen ts in 2- and 3-D problems, and then in the presence of noise and model ing errors. The results suggest that FOCUSS is a powerful algorithm wi th considerable utility for tomographic current estimation.