[MEG inverse solution using Gauss-Newton algorithm modified by Moore-Penrose inversion].
In magnetoencephalogram(MEG) basic studies, it is an important issue to estimate magnetic source parameters by inverse solution. It is known that the magnetic field equations are nonlinear, thus explicit solutions are difficult to obtain. However optimization methods are available to this parameter estimation. In many usually used nonlinear local optimization algorithms, Gauss-Newton's is of fast convergent speed. When this algorithm is used, the singularity of the Jacobien matrix about the minimum least square error must be considered carefully. If the matrix is singular, the equation for searching direction has no general solution. One way to overcome this problem is to use negative gradient as searching direction, but it may cause descent of convergent speed. Another way is known as Levenberg-Marquardt algorithm which makes the matrix non-singular by adding some improved factors to it. In this paper we utilize Moore-Penrose inversion for the solution of iterative searching direction equation. In appendix we demonstrate that the searching direction obtained by the proposed method is successful. Computer simulation also demonstrates that by reasonable selection of initial iterative values, the modified Gauss-Newton algorithm is effective for MEG inverse solution in the case with one or two source dipoles.
Li
J
J
State Key Laboratory of Modern Optical Instrumentation, Center for Optical and Electromagnetic Research, Zhejiang University, Hangzhou 310027.
D000465:Algorithms; D003198:Computer Simulation; D015225:Magnetoencephalography / Q000379:methods*; D008962:Models, Theoretical; D009716:Numerical Analysis, Computer-Assisted