Ill-posed MEG inverse solution based on deterministic regularization theory framework

Magnetoencephalographic (MEG) source reconstruction is physically ill-posed, regularization is therefore necessary adding a priori constraint to make it well-posed. Using distributed source model, this imaging problem can be formulated as an ill-conditioned and highly underdetermined linear inverse problem. In this paper, the proposed a modified method, which we call a region weighing method, is based on the minimum norm estimation with Tikhonov regularization, imposing constraints assumptions on the solution from the viewpoint of the mathematical nature and anatomical and physiological knowledge. In order to obtain unique and physiologically justified solution, an operator of region weighing is introduced, meanwhile incorporating the depth weighing in the reconstruction procedure. Computer experiments show the method presented here is promising.