A Comparative Study of Minimum Norm Inverse Methods for MEG Imaging

Abstract

The majority of MEG imaging techniques currently in use fall into the general class of (weighted) minimum norm methods. The minimization of a norm is used as the basis for choosing one from a generally infinite set of solutions that provide an equally good fit to the data. This ambiguity in the Solution arises from the inherent non-unique-ness of the continuous inverse problem and is compounded by the imbalance between the relatively small number of measurements and the large number of source voxels. Here we present a unified view of the minimum norm methods and describe how we can use Tikhonov regularization to avoid instabilities in the solutions due to noise. We then compare the Performance of regularized versions of three well known linear minimum norm methods [51 [7] with the non-linear iteratively reweighted minimum norm method [11 and a Bayesian approach described in our companion paper (“MEG-based Imaging of Focal Neuronal Current Sources,” Phillips J.W., Leahy R.M., Mosher J.C.).KeywordsMinimum NormTikhonov RegularizationBayesian TechniquePhantom DataMagnetic Source ImageThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.