If. Gorodnitsky et al., NEUROMAGNETIC SOURCE IMAGING WITH FOCUSS - A RECURSIVE WEIGHTED MINIMUM NORM ALGORITHM, Electroencephalography and clinical neurophysiology, 95(4), 1995, pp. 231-251
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.