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Standardized low-resolution brain electromagnetic tomography (sLORETA): technical details.

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TLDR
The technical details of the method are presented, allowing researchers to test, check, reproduce and validate the new method, and a solution reported here yields images of standardized current density with zero localization error.
Abstract
Scalp electric potentials (electroencephalograms) and extracranial magnetic fields (magnetoencephalograms) are due to the primary (impressed) current density distribution that arises from neuronal postsynaptic processes. A solution to the inverse problem--the computation of images of electric neuronal activity based on extracranial measurements--would provide important information on the time-course and localization of brain function. In general, there is no unique solution to this problem. In particular, an instantaneous, distributed, discrete, linear solution capable of exact localization of point sources is of great interest, since the principles of linearity and superposition would guarantee its trustworthiness as a functional imaging method, given that brain activity occurs in the form of a finite number of distributed hot spots. Despite all previous efforts, linear solutions, at best, produced images with systematic nonzero localization errors. A solution reported here yields images of standardized current density with zero localization error. The purpose of this paper is to present the technical details of the method, allowing researchers to test, check, reproduce and validate the new method.

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References
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Journal ArticleDOI

Nonparametric permutation tests for functional neuroimaging: A primer with examples

TL;DR: The standard nonparametric randomization and permutation testing ideas are developed at an accessible level, using practical examples from functional neuroimaging, and the extensions for multiple comparisons described.
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Low resolution electromagnetic tomography: a new method for localizing electrical activity in the brain.

TL;DR: A direct comparison of the tomography results with those obtained from fitting one and two dipoles illustrates that the new method provides physiologically meaningful results while dipolar solutions fail in many situations.
Book

Inverse Problem Theory: Methods for Data Fitting and Model Parameter Estimation

TL;DR: In this paper, the least-squares (l 2 -norm) and the Minimax (l #-norm) Criterion are introduced. But they do not cover the general discrete inverse problem.
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