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Backus and Gilbert method for vector fields.

R Grave de Peralta Menendez1, S L Gonzalez Andino

  • 1Department of Neurology, Geneva University Hospital, Switzerland. grave@diogenes.hcuge.ch

Human Brain Mapping
|April 9, 1999
PubMed
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This study details the Backus and Gilbert theory for vector fields in electromagnetic inverse problems. It provides a novel mathematical derivation and discusses potential misuse and limitations, offering alternative solutions.

Area of Science:

  • Geophysics
  • Electromagnetism
  • Inverse Problems

Background:

  • The Backus and Gilbert theory is a foundational method for solving inverse problems.
  • Electromagnetic inverse problems require the retrieval of vector fields.

Purpose of the Study:

  • To describe the Backus and Gilbert theory specifically for vector fields.
  • To present a detailed mathematical derivation for retrieving vector fields.
  • To identify potential misuses and disadvantages of the theory for vector fields.

Main Methods:

  • Detailed mathematical derivation of coefficients for vector field retrieval.
  • Analysis of the Backus and Gilbert theory's application to vector fields.

Main Results:

Related Experiment Videos

  • A novel mathematical derivation for vector field retrieval using Backus and Gilbert theory is presented.
  • Crucial points leading to potential misuse of the solution are identified.
  • Disadvantages of the theory for vector fields are discussed.

Conclusions:

  • The report provides a comprehensive understanding of the Backus and Gilbert theory for vector fields.
  • It offers a new derivation and highlights critical considerations for its application.
  • Alternative approaches are suggested to overcome the theory's limitations.