Abstract
A major goal in biomagnetism is the reconstruction of current distributions without making preliminary assumptions about number and temporal properties of the sources to be reconstructed. We propose a new current density reconstruction method that computes source images with high resolution and small blurring. A nonlinear functional, the L1-norm, is used as a source constraint. The L1-norm is the sum of absolute current densities. A simple Simulation shows, that the L1-norm does neither impose artificial smoothness nor sharpness upon the reconstructed sources. We have implemented three different minimization schemes for the L1-norm, which we compare against each other and against the MNLS (minimum norm least squares, L2-norm) method [1]. Unlike the L1-norm method described earlier [2], our approaches tolerate noisy data and arbitrary source orientations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Wang, J.Z., Williamson, S.J., Kaufmann, L., Magnetic source images determined by a lead-field analysis: the unique minimum-norm least-squares estimation, IEEE Trans. Biomed. Eng., 1992, 39: 665–675.
Matsuura, K., Okabe, Y., Selective minimum-norm Solution of the biomagnetic inverse problem, IEEE Trans. Biomed. Eng., 1995, 42: 608–615.
Fuchs, M., Wagner, M., Wischmann, H.-A., Generalized minimum norm least squares reconstruction algorithms, ISBET Newsletter (ISSN 0947–5133), 1994, (5):8-l 1.
Wagner, M., Fuchs, M., Wischmann, H:-A., Ottenberg, K., Dössel, O., Cortex segmentation from 3D MR images for MEG reconstructions, In: C. Baumgartner et al, Biomagnetism: fundamental research and clinical applications, Amsterdam, Elsevier/IOS Press, 1995, 433–438.
Meijs, J.H.W., Weier, O.W., Peters, M.J., van Oosterom, A., On the numerical accuracy of the boundary element method, IEEE Trans. Biomed. Eng., 1989, 36: 1038–1049.
Kuenzi, H.P., Tzschach, H.G., Zehnder, C.A., Numerical methods of mathematical optimization, New York, Academic Press, 1971.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media New York
About this paper
Cite this paper
Wagner, M., Wischmann, HA., Fuchs, M., Köhler, T., Drenckhahn, R. (2000). Current Density Reconstructions Using the L1 Norm. In: Aine, C.J., Stroink, G., Wood, C.C., Okada, Y., Swithenby, S.J. (eds) Biomag 96. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1260-7_96
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1260-7_96
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7066-9
Online ISBN: 978-1-4612-1260-7
eBook Packages: Springer Book Archive