Biomag 96 pp 393-396 | Cite as

Current Density Reconstructions Using the L1 Norm

  • M. Wagner
  • H.-A. Wischmann
  • M. Fuchs
  • T. Köhler
  • R. Drenckhahn

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.

Keywords

Covariance 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [11.
    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.CrossRefGoogle Scholar
  2. [2]
    Matsuura, K., Okabe, Y., Selective minimum-norm Solution of the biomagnetic inverse problem, IEEE Trans. Biomed. Eng., 1995, 42: 608–615.CrossRefGoogle Scholar
  3. [3]
    Fuchs, M., Wagner, M., Wischmann, H.-A., Generalized minimum norm least squares reconstruction algorithms, ISBET Newsletter (ISSN 0947–5133), 1994, (5):8-l 1.Google Scholar
  4. [4]
    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.Google Scholar
  5. [5]
    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.CrossRefGoogle Scholar
  6. [6]
    Kuenzi, H.P., Tzschach, H.G., Zehnder, C.A., Numerical methods of mathematical optimization, New York, Academic Press, 1971.Google Scholar

Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • M. Wagner
    • 1
  • H.-A. Wischmann
    • 1
  • M. Fuchs
    • 1
  • T. Köhler
    • 1
  • R. Drenckhahn
    • 1
  1. 1.Philips Research HamburgHamburgGermany

Personalised recommendations