Abstract
A simple mathematical model used in the first commercial scanners for the biomagnetic imaging problem is considered. We discuss the restrictions in the resolution inherent in the mathematical model. It is shown that only the position of the dipole is computable not its strength. An approximate inversion formula is derived which results in a very efficient algorithm.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Golub, G.H., Pereyra, V.: The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate. SIAM J. Numer. Anal. 10 (1973) 413–432
Gudden, F., Hoenig, E., Reichenberger, H., Schittenhelm, R., Schneider, G.: Ein Vielkanalsystem zur Biomagnetischen Diagnostik in Neurologie und Kardiologie: Prinzip, Methode und erste Ergebnisse. electromedica 57 (1989) 2–7
Lemarié, P.G.(ed.): Les Ondelettes en 1989. Springer LNM 1438, Berlin 1990
Louis, A.K.: Inverse und schlecht gestellte Probleme. Teubner, Stuttgart, 1989
Louis, A.K., Maaß, P.: A mollifier method for linear operator equations of the first kind. Inverse Problems 6 (1990) 427–440
Robinson, S.E.: Theory and properties of lead field synthesis analysis. Proc. of the 7th International Conference on Biomagnetism, 14–18 Aug 1989, New York, 35–36
Sarvas, J.: Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem. Phys. Med. Biol. 32 (1987) 11–22
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Louis, A.K. (1991). Mathematical questions of a biomagnetic imaging problem. In: Herman, G.T., Louis, A.K., Natterer, F. (eds) Mathematical Methods in Tomography. Lecture Notes in Mathematics, vol 1497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084513
Download citation
DOI: https://doi.org/10.1007/BFb0084513
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54970-3
Online ISBN: 978-3-540-46615-4
eBook Packages: Springer Book Archive