Novel Fourier methods for biomagnetic boundary value problems

Abstract

A novel Fourier technique for solving a wide variety of boundary value problems is introduced. The technique, called Fourier projection, is based on the geometric properties of vector calculus operators in reciprocal space. Fourier projection decomposes arbitrary vector fields into collections of irrotational and/or divergenceless dipole subfields. For well-posed problems, Fourier projection algorithms can calculate unknown field values from a knowledge of primary sources and boundary conditions. Specifically, this technique is applied to several problems associated with biomagnetic imaging, including volume current calculations and equivalent surface current solutions. In addition, a low-cost magnetic field mapping system designed to aid reconstruction algorithm development is described.