Mathematical analysis of lead field expansions
Mathematical analysis of lead field expansions
复制标题
前导域扩展的数学分析
DOI：
10.1109/42.759120
复制
发表时间：
1999
影响因子：
10.6
通讯作者：
H. Müller
中科院分区：
文献类型：
--
作者：
John G. Taylor;A. Ioannides;H. Müller
生物电磁逆问题的解决方案根据广义导联场展开进行讨论，扩展到与电流强度相关的多项式权重。展开系数是从将前导场展开与数据相关联的所得方程组中获得的。该框架支持一系列算法，其中包括最小范数解类和加权最小范数解，包括经过适当修改以符合旋转不变性要求的FOCUSS（FOCal 欠定系统求解器）。详细讨论了加权最小范数族，明确了加权方案对未知电流密度矢量的模的依赖性（或独立性）。对于除线性情况之外的所有情况，并且权重为单一幂，都会产生高度非线性的方程组。对这些方程进行分析，并将它们的解简化为有限数量自由度的可处理问题。在最简单的磁场断层扫描（MFT）情况下，这被证明具有局部分布式源的预期特性。敏感性分析支持了这一结论。
The solution to the bioelectromagnetic inverse problem is discussed in terms of a generalized lead field expansion, extended to weights depending polynomially on the current strength. The expansion coefficients are obtained from the resulting system of equations which relate the lead field expansion to the data. The framework supports a family of algorithms which include the class of minimum norm solutions and those of the weighted minimum norm, including FOCUSS (FOCal Underdetermined System Solver), suitably modified to conform to the requirements of rotational invariance. The weighted minimum norm family is discussed in some detail, making explicit the dependence (or independence) of the weighting scheme on the modulus of the unknown current density vector. For all but the linear case, and with a single power in the weight, a highly nonlinear system of equations results. These equations are analyzed and their solution is reduced to tractable problems for a finite number of degrees of freedom. In the simplest magnetic field tomography (MFT) case, this is shown to possess expected properties for localized distributed sources. A sensitivity analysis supports this conclusion.
DOI：
10.1016/0013-4694(95)00107-a
发表时间：
1995-10-01
期刊：
ELECTROENCEPHALOGRAPHY AND CLINICAL NEUROPHYSIOLOGY
影响因子：
--
作者：
GORODNITSKY, IF;GEORGE, JS;RAO, BD
通讯作者：
RAO, BD