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Mathematical Problems in Engineering
Volume 2013, Article ID 413980, 15 pages
Research Article

Algebraic Reconstruction of Current Dipoles and Quadrupoles in Three-Dimensional Space

Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-8656, Japan

Received 27 July 2012; Accepted 28 December 2012

Academic Editor: Valery Yakhno

Copyright © 2013 Takaaki Nara. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents an algebraic method for an inverse source problem for the Poisson equation where the source consists of dipoles and quadrupoles. This source model is significant in the magnetoencephalography inverse problem. The proposed method identifies the source parameters directly and algebraically using data without requiring an initial parameter estimate or iterative computation of the forward solution. The obtained parameters could be used for the initial solution in an optimization-based algorithm for further refinement.