On Minimal lp-Norm Solutions of the Biomagnetic Inverse Problem

In this paper we investigate the properties of minimal lp-norm solutions to the biomagnetic inverse problem for 1 <= p <2. We show that the minimal l1-norm solutions can be interpreted as weighted l2-norm solutions, where the weights emphasize the larger currents and make the minimal l1-norm solutions appear more focal than the minimal l2-norm solutions. In several examples we demonstrate that the current distribution changes continuously as the parameter p varies. Finally, a short overview about related work in robust statistics is given

Temporal and Spatial Prewhitening of Multi-Channel MEG Data

In this paper we present a prewhitening strategy to decorrelate the noise in space and in time. We discuss in detail how the effects of the filtering can be seen in the singular value decomposition of the data and we demonstrate how the approach can be used with an objective, statistical signal subspace estimation algorithm

Objective Signal Subspace Determination for MEG

In statistical signal processing many tests have been proposed to determine the dimension of the signal subspace. In MEG the problem of signal subspace determination arises when multiple-dipole fitting methods are used for source reconstruction. To find an objective and automatic method for determining the signal subspace dimension, in contrast to the common method of visual inspection of a singular value spectrum, we investigated the behavior of the statistical test proposed by Xu et al.. In this paper we characterized the essential statistical quantity for correct detection, evaluated the test under realistic conditions, and analyzed the behavior of the test when applied to real MEG data