Localization of Extended Sources Using a Modified Linear Estimation Approach

Abstract

Biomagnetic measurements using multichannel systems provide magnetic data sets for functional localization of heart or brain activity non-invasively. The interpretation of measured magnetic fields generated by the electrical active organs requires special algorithms to localize or reconstruct the sources. Numerous optimization algorithms to solve this inverse problem are under consideration, deterministic as well as stochastic one. In most cases non-linear, deterministic optimization procedures like Levenberg-Marquardt algorithm are used. We have found that Marquardt algorithm combined with Gauss-Seidel-iteration is the best inverse Solution method in least-squares sense to localize up to three single dipoles [1]. But there appear problems with convergence of this method if deep lying or extended sources have to be localized. For these cases we developed a new version of the well-known minimum-norm Solution based on the Linear Estimation Theory [2,3]. We introduced some modifications which enable us to reconstruct distributed sources too [4]. Therefore, the aim of this paper is to propose a new method for reconstruction of extended sources and estimating their extension.