Brain Topography

, Volume 9, Issue 2, pp 117–124 | Cite as

Figures of merit to compare distributed linear inverse solutions

  • Rolando Grave de Peralta Menendez
  • Sara L. Gonzalez Andino
  • Bernd Lütkenhöner
Article

Summary

This paper introduces the concept of the resolution matrix as the basis for an objective theoretical comparison of distributed linear inverse solutions to the neuroelectromagnetic inverse problem. In particular, we describe how figures of merit derived from the resolution matrices can be represented graphically to evaluate merits and shortcomings of the different solutions. The use of the figures of merit is illustrated with two solutions that consider minimal a priori information about the generators: Classical Minimum Norm and Backus Gilbert. We recommend to start any analysis with the individual exploration of the resolution kernel for each grid point or at least for those points where the activity is likely to occur. This analysis might help in selecting the optimal inverse for the sources that are supposed to be active in the process under study.

Key words

Distributed solutions Inverse problem Distributed source models Figures of merit 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Backus, G.E. and Gilbert, J.F. Numerical applications of a formalism for geophysical inverse problems. Geophys. J. Roy. Astron. Soc. 1967, 13:247–276.Google Scholar
  2. Backus, G.E. and Gilbert, J.F. The resolving power of gross earth data. Geophys. J. Roy. Astron. Soc. 1968, 16:169–205.Google Scholar
  3. Backus, G.E. and Gilbert, J.F. Uniquenness in the inversion of gross earth data. Phil. Trans. R. Soc. 1970, 266:123–192.Google Scholar
  4. Bertero, M., De Mol, C., Pike, E.R. Linear inverse problems with discrete data. I: General formulation and singular system analysis. Inverse Problem, 1985, 1: 301–330.Google Scholar
  5. Brenner, D., Williamson, S.J. and Kauffman, L. Visually evoked magnetic fields of the human brain. Science, 1975, 190: 480–481.PubMedGoogle Scholar
  6. Greenblatt, R.E. Probabilistic reconstruction of multiple sources in the neuroelectromagnetic inverse problem. Inverse Problems, 1993, 9: 271–284.Google Scholar
  7. Hämäläinen, M.S. and Ilmoniemi, R.J. Interpreting measured magnetic fields of the brain: Estimates of Current Distributions., Technical Report TKK-F-A559, Helsinski University of Technology, 1984.Google Scholar
  8. Hämäläinen, M. Interpretation of Neuromagnetic measurements: Modeling and Statistical Considerations. Ph. D. Thesis, Espoo, Finland, 1987.Google Scholar
  9. Ilmoniemi, R.J. Estimates of Neuronal Current Distributions. Acta Otolaryngol (Stockh). 1991, Suppl, 491: 80–87.Google Scholar
  10. ISBET Newsletter. No 5. November 1994. Ed. W. Skrandies.Google Scholar
  11. Jackson, D.D. Interpretation of Inaccurate, Insufficient and Inconsistent data. Geophys. J. Roy. Astron. soc., 1972, 28:97–110.Google Scholar
  12. Menke, W. Geophysical Data Analysis: Discrete inverse theory. Academic Press, 1984.Google Scholar
  13. O'Sullivan F. A Statistical perspective on ill-posed inverse problems. 1986, 1. No. 4, 502–527.Google Scholar
  14. Peng, C., Rodi, W. and Toksoz, M.N. Smoothest-model reconstruction from projections. Inverse Problem, 1993, 9:339–354.Google Scholar

Copyright information

© Human Sciences Press, Inc 1996

Authors and Affiliations

  • Rolando Grave de Peralta Menendez
    • 1
  • Sara L. Gonzalez Andino
    • 1
  • Bernd Lütkenhöner
    • 1
  1. 1.Institute fur Experimentelle AudiologieUniversitat MunsterMunsterGermany

Personalised recommendations