Meg Inverse Problem Of Magnetic Source Reconstruction Algorithm

Magnetoencephalography(MEG), measurement of neuromagnetic fields by superconducting quantum interference devices (SQUIDs), is a useful noninvasive method for investigating human brain functions. The core of MEG research is its inverse problem obtaining the underlying neural activity from the magnetic field measured outside a human head. The scope of this paper is focus on the inverse problem solution. The author has done the following research work:Firstly, the basic mathematical theory and electromagnetic concepts are thoroughly discussed, including general Maxwell equations and the quasistatic approximation on bioelectromagnetic studies. Meanwhile, MEG forward problem is analysis in general ways.Secondly, an overview is given on the solution method for MEG inverse problem. During the development of inverse problem research, the source reconstruction methods are classified as dipole source localization and source imaging (or current density reconstruction). The former, applying the point source model, leads to a nonlinear inverse problem. And the latter, applying the distributed source model, can be cast a linear problem.In dipole localization based on point source model, we proposed a synthetic algorithm, which vary the used optimization method during the source scanning procedure. We use quasi-Newton(QN) method for a high-speed coarse scan over a large area of the head, and Levenberg-Marquardt(LM) method for a fine scan near the source area. In comparison with those single optimization methods, this synthetic approach proved to be more efficient both in terms of computation time and sensitivity to the iterative initial value.MEG source image reconstruction, an important and difficult problem in image processing applications, is formulated as ill-posed inverse problem, so regularization is necessary. Regularization can be classified into two common approaches, i.e., deterministic and stochastic. Their common feature is that they both make use of a priori constraints concerning the current density distribution. In this paper we review several aspects of the application of regularization theory in MEG source image reconstruction, where the minimum norm estimation with Tikhonov regularization and Bayesian framework based on MAP-MRF model are introduced in detail. The characteristics, difference of these methods are also discussed.To our knowledge, there is no paper talking about the regularization for the MEG source image reconstruction from a unifying viewpoint. So we try to present a relative complete regularization viewpoint on this special imaging.In deterministic regularization, i.e., adopting minimum-norm estimation with Tikhonov regularization, we proposed the concept of region weighing. 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. And limitations of the proposed method and future work are then discussed.In stochastic regularization, we present a reconstruction method based on a Markovprior image model in order to obtain a stable solution, in this image model, the neural current density distributed image is extended to include not only the image vector of the moment values but also include the quantities corresponding to the image edges that are binary line processed. Thus the reconstruction is defined as the maximum a posteriori estimate(MAP) based on Bayesian framework. To acquire a global minimum solution from the posterior energy function, we here incorporate the ideas of coupled gradient artificial neural networks into this mixed integer optimization task.After the present study, some issues remain open. Next, we are going to achieve the improvements of our works. Finally, we discuss the major results of this paper and some comments on MEG future trends.