A comparison of iterative thresholding algorithms for the MEG inverse problem

The magnetoencephalography (MEG) aims at reconstructing the unknown electric activity in the brain from the measurements of the magnetic field in the outer space. The MEG inverse problem is ill-posed and/or ill-conditioned thus further constraints are needed to guarantee a unique and stable solution. Assuming that neural sources are confined in small regions of the brain, the sparsity assumption can be used as a regularization term. Thus, the solution of the inverse problem can be approximated by iterative thresholding algorithms. In order to identify an efficient inversion method for the MEG problem, we compare the performance -efficiency, accuracy, computational load- of some thresholding algorithms when localizing a single neural source. The numerical tests will give some suggestions on the construction of an efficient algorithm to be used in real life applications.