BASIC MATHEMATICAL AND ELECTROMAGNETIC CONCEPTS OF THE BIOMAGNETIC INVERSE PROBLEM
BASIC MATHEMATICAL AND ELECTROMAGNETIC CONCEPTS OF THE BIOMAGNETIC INVERSE PROBLEM
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DOI：
10.1088/0031-9155/32/1/004
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发表时间：
1987-01-01
影响因子：
3.5
通讯作者：
SARVAS, J
中科院分区：
文献类型：
--
作者：
SARVAS, J
本文综述了生物磁逆问题的基本数学和物理概念以及一些新的研究方法。讨论了均匀介质和非均匀介质的正演问题。给出了处理分段均匀导体的Geselowitz公式和表面积分方程。文中详细讨论了球对称导体和水平层状介质的特例。讨论了磁逆问题解的不唯一性，研究了电势对导体外磁场的贡献所造成的困难。作为求解该反问题的实用方法，讨论了带置信限的加权最小二乘搜索和最小范数估计方法。
Basic mathematical and physical concepts of the biomagnetic inverse problem are reviewed with some new approaches. The forward problem is discussed for both homogeneous and inhomogeneous media. Geselowitz'formulae and a surface integral equation are presented to handle a piecewise homogeneous conductor. The special cases of a spherically symmetric conductor and a horizontally layered medium are discussed in detail. The non-uniqueness of the solution of the magnetic inverse problem is discussed and the difficulty caused by the contribution of the electric potential to the magnetic field outside the conductor is studied. As practical methods of solving the inverse problem, a weighted least-squares search with confidence limits and the method of minimum norm estimate are discussed.