Comparing regularized and non-regularized nonlinear dipole fit methods: A study in a simulated sulcus structure

The inverse problem arising from EEG and MEG is largely underdetermined. On e strategy to alleviate this problem is the restriction to a limited number of point-like sources, the focal source model. Although the singular value decomposition of the spatio-temporal data gives an estimate of the minimal number of dipoles contributing to the measurement, the exact number is unk nown in advance and noise complicates the reconstruction Classical non-regu larized nonlinear dipole fit algorithms do not give an estimate for the cor rect number because they are not stable with regard to an overestimation of this parameter. Too many sources may only describe noise but can still att ain a large magnitude during the inverse procedure and may be indiscernible from the true sources. This paper describes a nonlinear dipole fit reconst ruction algorithm with a new regularization approach for the embedded linea r problem, automatically controlled by the noise in the data and the condit ion of the occuring least square problems. The algorithm is stable with reg ard to source components which "nearly" lie in the kernel of the projection or lead field operator and it thus gives an estimate of the unknown number parameter. EEG simulation studies in a simulated sulcus structure are carr ied out for an instantaneous dipole model and spatial resolution in the sul cus and stability of the new method are compared with a classical reconstru ction algorithm without regularization.