Use of group theory in the selection and description of regularization methods for functional source imaging

Abstract

Commonly, functional source imaging problems are "partial" rather than "ordinary" inverse problems--wherein the defining operator consists of component operators that individually do not address all variables of the unknown. When this ordinary-to-partial transition is minimally constrained, algebraic principles can be used to derive a favored methodology--which we do here. The resulting Isotropy method is compared to two other regularization methods proposed for functional source imaging (Kalman and Joint Regularization). This theoretical support for the favored status of the Isotropy method is consistent with its favorable computational performance in low prior information settings, as indicated in recent publications.