Discussing the Capabilities of Laplacian Minimization

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Abstract
This paper discusses the properties and capabilities of linear inverse solutions to the neuroelectromagnetic inverse problem obtained under the assumption of smoothness (Laplacian Minimization). Simple simulated counterexamples using smooth current distributions as well as single or multiple active dipoles are presented to refute some properties attributed to a particular implementation of the Laplacian Minimization coined LORETA. The problem of the selection of the test sources to be used in the evaluation is addressed and it is demonstrated that single dipoles are far from being the worst test case for a smooth solution as generally believed. The simulations confirm that the dipole localization error cannot constitute the tool to evaluate distributed inverse solutions designed to deal with multiple sources and that the necessary condition for the correct performance of an inverse is the adequate characterization of the source space, i.e., the characterization of the properties of the actual generators.

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