Magnetoencephalography source localization using improved simplex method

Nelder-Mead downhill simplex method, a kind of deterministic optimization algorithms, has been used extensively for magnetoencephalography (MEG) dipolar source localization problems because it does not require any functional differentiation. Like many other deterministic algorithms, however, it can be easily trapped in local optima when being applied to complex inverse problems with multiple simultaneous sources. In the present study, some modifications have been made to improve its capability of finding global optima. Those include (1) constructing an initial simplex based upon sensitivity of variables and (2) introducing a shaking technique based on polynomial interpolation. The efficiency of the proposed method was tested using analytical test functions and simulated MEG data. The simulation results demonstrate that the improved downhill simplex method can result in more reliable inverse solutions than the conventional one.