Brain Topography

, Volume 13, Issue 2, pp 97–104

Discussing the Capabilities of Laplacian Minimization

  • Rolando Grave de Peralta Menendez
  • Sara L. Gonzalez Andino


This paper discusses the properties and capabilities of linear inverse solutions to the neuroelectromagnetic inverse problem obtained under the assumption of smoothness (Laplacian Minimization). Simple simulated counterexamples using smooth current distributions as well as single or multiple active dipoles are presented to refute some properties attributed to a particular implementation of the Laplacian Minimization coined LORETA. The problem of the selection of the test sources to be used in the evaluation is addressed and it is demonstrated that single dipoles are far from being the worst test case for a smooth solution as generally believed. The simulations confirm that the dipole localization error cannot constitute the tool to evaluate distributed inverse solutions designed to deal with multiple sources and that the necessary condition for the correct performance of an inverse is the adequate characterization of the source space, i.e., the characterization of the properties of the actual generators.

Linear inverse solutions Laplacian minimization 


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  1. Alarcon, G., Guy, C.N., Binnie, C.D., Walker, S.R., Elwes, R.D.C. and Polkey, C.E. Intracerebral propagation of interictal activity in partial epilepsy: implications for source localisation. J. Neurol. Neurosurg. Psychiatry, 1994, 57: 435-449.Google Scholar
  2. Backus, G.E. and Gilbert, J.F. The resolving power of gross earth data. Geophys. J.R. Astron. Soc. 1968, 16: 169-205.Google Scholar
  3. Fuchs, M. Wischmann, H. A. and Wagner, M. Generalized minimum norm least squares reconstruction algorithms. In: W. Skrandies (Ed.), ISBET Newsletter, No. 5, 1994: 8-11.Google Scholar
  4. Golberg, M.A., (Ed.). Solution Methods for Integral Equations, Plenum Press, New York, 1978.Google Scholar
  5. Grave de Peralta Menendez, R., Hauk, O., Gonzalez Andino, S., Vogt, H. and Michel, C.M. Linear inverse solutions with optimal resolution kernels applied to the electromagnetic tomography. Human Brain Mapping 5, 1997: 454-467.Google Scholar
  6. Grave de Peralta Menendez, R. and Gonzalez Andino, S.L. A critical analysis of linear inverse solutions. IEEE Trans. Biomed. Eng., 1998, 4: 440-448.Google Scholar
  7. Grave de Peralta Menendez, R., Gonzalez Andino, S.L., Morand, S., Michel, C.M. and Landis, T.M. Imaging the electrical activity of the brain: ELECTRA. Human Brain Mapping, 2000, 1: 12.Google Scholar
  8. Greenblatt, R. Some comments on LORETA. In: W. Skrandies (Ed.), ISBET Newsletter, No. 5, 1994: 11-13.Google Scholar
  9. Groetsch, C.W. The theory of Tihonov regularization for Fredholm equations of first kind. Pitman Publishing Ltd. 1984.Google Scholar
  10. Hamalainen, M. Discrete and distributed source estimates. In: W. Skrandies (Ed.), ISBET Newsletter, No. 6, 1995: 9-12.Google Scholar
  11. Huiskamp, G. and van Oosterom, A. The depolarization sequence of the human heart surface computed from measured body surface potentials. IEEE Trans. Biomed. Eng., 1988; 35:1047-1058.Google Scholar
  12. Ilmoniemi, R.J. Estimating brain source distributions: Comments on LORETA. In: W. Skrandies (Ed.), ISBET Newsletter, No. 6, 1995: 12-14.Google Scholar
  13. Lütkenhönner, B. and Grave de Peralta Menendez, R. The resolution field concept. Electroencephalography and Clinical Neurophysiology, 1997, 102: 326-334.Google Scholar
  14. Menke, W. Geophysical data analysis: Discrete inverse theory. Academic Press. San Diego, 1989.Google Scholar
  15. Messinger-Rapport, B.J. and Rudy, Y. Regularization of the inverse problem in electrocardiography: a model study. Math Biosci., 1998, 89: 79-118.Google Scholar
  16. Mosher, J.C. and George, J.S. Comments on LORETA. In: W. Skrandies (Ed.), ISBET Newsletter, No. 5, 1994: 14-17.Google Scholar
  17. Nunez, P.L. Comments on LORETA. In: W. Skrandies (Ed.), ISBET Newsletter, No. 6, 1995: 14-16.Google Scholar
  18. Pascual Marqui, R.D., Michel, C.M. and Lehmann, D. Low resolution electromagnetic tomography: a new method for localizing electrical activity in the brain. Int. J. Psychophysiol., 1995, 18: 49-65.Google Scholar
  19. Tihonov, A.N. and Arsenin, V.Y. Solutions of ill-posed problems. Wiley, New York, 1997.Google Scholar
  20. Valdes, P. Grave de Peralta, R. and Gonzalez, S. Comment on LORETA. In: W. Skrandies (Ed.), ISBET Newsletter, No. 5, 1994: 18-21.Google Scholar
  21. van Oosterom, A. History and evolution of methods for solving the inverse problem. J. Clinical Neurophysiology, 1992, 8: 371-380.Google Scholar
  22. Wagner, M., Fuchs, M., Wischmann, H.A., Drenckhahn, R. and Köhler, T. Smooth reconstructions of cortical sources from EEG and MEG recordings. Neuroimage, 1996, 3: 168.Google Scholar
  23. Wahba, G. Spline models for observational data. Society for Industrial and applied mathematics. Philadelphia, Pennsylvania, 1990.Google Scholar

Copyright information

© Human Sciences Press, Inc. 2000

Authors and Affiliations

  • Rolando Grave de Peralta Menendez
    • 1
  • Sara L. Gonzalez Andino
    • 1
  1. 1.Functional Brain Mapping Lab.,University Hospital Geneva,Switzerland

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