Characteristic bodies and surface constrained source estimation

William J. Dallas

doi:10.1117/12.130909

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9 December 1992 Characteristic bodies and surface constrained source estimation

William J. Dallas

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Proceedings Volume 1768, Mathematical Methods in Medical Imaging; (1992) https://doi.org/10.1117/12.130909
Event: San Diego '92, 1992, San Diego, CA, United States

Abstract

The characteristic body is a mathematical tool developed for use in radar imaging. In this paper we extend its use to the seemingly divergent fields of biomagnetic imaging and optical propagation. Biomagnetic imaging is the estimation of electrical current flows that give rise to quasi-static magnetic fields surrounding biological organisms. This estimation incorporates measurements of the field and constraints derived from a priori knowledge and from ad hoc assumptions. One of the interesting constraints is confinement of the electrical-current sources to a surface such as that of the brain's cortex. By combining an appropriate characteristic body with Maxwell's equations and the 3-D vector Fourier transform, an algorithm for calculating the source currents presents itself quite naturally. We show how various constraints can be introduced into this reconstruction process through characteristic bodies. In addition, we show how the formalism can provide a framework for describing optical propagation and diffraction.

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William J. Dallas "Characteristic bodies and surface constrained source estimation", Proc. SPIE 1768, Mathematical Methods in Medical Imaging, (9 December 1992); https://doi.org/10.1117/12.130909

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