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A unified weighted minimum norm solution for the reference inverse problem in EEG.

Ricardo A Salido-Ruiz1, Radu Ranta2, Gundars Korats3

  • 1University of Guadalajara, Department of Computer Science in the University Center for Exact Sciences and Engineering (CUCEI), Guadalajara, Jalisco, Mexico.

Computers in Biology and Medicine
|October 25, 2019
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Summary

The study shows that both Average Reference (AR) and Reference Standardization Technique (REST) for electroencephalography (EEG) recordings can be derived from a general inverse problem formalism. AR is a minimum norm solution, while REST is a weighted minimum norm solution.

Keywords:
EEGInverse problemsReference potential

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Area of Science:

  • Neuroscience
  • Biomedical Engineering
  • Signal Processing

Background:

  • The choice of reference electrode significantly impacts electroencephalography (EEG) recordings.
  • Average Reference (AR) and Reference Standardization Technique (REST) are widely accepted as optimal solutions for EEG reference.
  • Existing research primarily focuses on comparing AR and REST, with less emphasis on their theoretical underpinnings.

Purpose of the Study:

  • To demonstrate that both AR and REST can be derived from a unified inverse problem formalism for reference estimation.
  • To provide a novel derivation supporting existing theoretical findings on AR and REST.
  • To reinforce the understanding of AR as a specific instance of REST within a broader framework.

Main Methods:

  • Utilized a least squares approach to derive reference estimation techniques.
  • Formulated reference estimation as a general inverse problem.
  • Re-derived AR and REST using an alternative mathematical approach.

Main Results:

  • Confirmed that AR represents the minimum norm solution within the inverse problem framework.
  • Showed that REST is a weighted minimum norm solution incorporating an approximate propagation model.
  • Established that AR is a particular case of REST, reinforcing their relationship.

Conclusions:

  • AR and REST are not independent methods but are unified under a general inverse problem formalism.
  • The least squares derivation provides strong evidence for the theoretical relationship between AR and REST.
  • This work offers a new perspective on EEG reference electrode selection and its theoretical basis.