摘要
在脑磁图的理论研究中 ,通过求解脑磁逆问题以确定磁源参数是一个重要的问题。由于磁场方程为非线性方程 ,难以给出解析解。而利用最优化方法可以对这种源参数进行估计。在多种常用的非线性局域优化算法中 ,高斯 -牛顿算法具有较快的收敛速度。在采用这种算法计算时 ,须考虑关于最小二乘残差的雅可比矩阵的奇异性问题。一般情况下 ,出现奇异时 ,一种修正方法是采用负梯度方向作为迭代方向 ,这样可能造成收敛速度的下降 ;另一种被称为 L evenberg- Marquardt方法的 ,是通过在矩阵中增加一些修正因子 ,来改善矩阵性质使之非奇异。这里采用一种基于 Moore- Penrose广义逆的修正方法 ,并证明了这种方法可以保证成功的迭代搜索方向。模拟计算表明 :在合理选择迭代初始值的条件下 ,对于只有一两个偶极子源的情况 ,这一修正的高斯
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 appen dix 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.
出处
《生物医学工程学杂志》
EI
CAS
CSCD
2001年第2期265-268,共4页
Journal of Biomedical Engineering
基金
国家自然科学基金资助项目 (5 99470 0 4)
关键词
脑磁图
逆问题
MOORE-PENROSE广义逆
高斯-牛顿算法
Algorithms
Biomedical engineering
Computer simulation
Iterative methods
Matrix algebra
Optimization
Parameter estimation
