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Biomagnetic Imaging: A View From Fourier Space

Biomagnetic imaging is the estimation of electrical activity patterns in humans and animals from measurements of the magnetic fields this electrical activity generates. We concentrate our attention here on the mathematical procedures used to form these estimates. In particular, Fourier transforms will be used extensively to provide intuitive descriptions of these procedures. We present a very abbreviated history of biomagnetic imaging followed by descriptions of magnetic field generation. We show how Fourier transforms can be used to develop a transfer function description of imaging system properties as well as simplifying reconstruction algorithms. Finally, the problem of magnetic field extrapolation from limited sets of measurements is discussed and a Fourier transform based solution is presented.