Penalized Least Squares methods for solving the EEG Inverse Problem

Statistica Sinica

Volumn 18, Issue 4, 2008, Pages 1535-1551

  Vega Hernández, Mayrim ^a   Martínez Montes, Eduardo ^a   Sánchez Bornot, José M ^a   Lage Castellanos, Agustín ^a   Valdés Sosa, Pedro A ^a  

^a CUBAN NEUROSCIENCE CENTER   (Cuba)

Author keywords

EEG; Inverse Problem; Least Squares; Penalized regression

Indexed keywords

EID: 60149096965     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (36)

1. Bosch-Bayard, J., Valdés-Sosak, P., Virués-Alba, E., Aubert-Vázquez, E., John, E. R., Harmony, T., Riera-Díaz, J. and Trujillo-Barreto, N. (2001). 3D statistical parametric mapping of variable resolution electromagnetic tomography (VARETA). Clin. Electroencephal. 32, 47-66.
2. Carbonell, F., Galán, L., Valdés-Sosa, P., Worsley, K., Biscay, R. L., Díaz-Comas, L., Bobes, M. A. and Parra, M. (2004). Random field-union intersection tests for EEG/MEG imaging. Neurolmage. 22, 268-276.
3. Craven, P. and Wahba, G. (1979). Smoothing noisy data with spline functions: estimating the correct degree of smoothing by the method of generalized cross-validation. Numer. Math. 31, 377-403.
4. Delorme, A. and Makeig, S. (2004). EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics including independent component analysis. J. Neurosci. Meth. 134, 9-21.
5. Di Russo, F., Martínez, A., Sereno, I. M., Pitzalis, S. and Hillyard, S. A. (2001). Cortical sources of the early components of the visual evoked potential. Hum. Brain Mapp. 15, 95-111.
6. Evans, A. C, Collins, D. L., Mills, S. R., Brown, E. D., Kelly, R. L. and Peters, T. M. (1993). 3D statistical neuroanatomical models from 305 MRI volumes. Proc. IEEE-Nuclear Science Symposium and Medical Imaging Conference. 95, 1813-1817. M.T.P Press, London.
7. Fan, J. Q. and Li, R. Z. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. J. Amer. Statist. Assoc. 96, 1348-1360.
8. Fuchs, M., Wagner, M., Wischman, H. A. and Dossel, O. (1995). Cortical current imaging by morphologically constrained reconstructions. In Biomagnetism: Fundamental Research and Clinical Applications (Edited by C. Baumgartner, et al.), 320-325, Elsevier: Science IOS Press.
9. Fuchs, M., Wagner, M., Kohler, T. and Wischman, H. A. (1999). Linear and nonlinear current density reconstructions. J. Clin. Neurophysiol. 16, 267-295.
10. Grave de Peralta, R. and González, S. L. (1998). Basic limitations of linear inverse solutions: a case study. IEEE Eng. Med. Biol. 4, 2143-2146.
11. Gorodnitsky, I. F. and Rao, B. D. (1997). Sparse signal reconstruction from limited data using FOCUSS: are-weighted minimum norm algorithm. IEEE T Signal Proces. 45, 600-616.
12. Golub, G., Heath, M. and Wahba, G. (1979). Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 21, 215-223.
13. Hadamard, J. (1923). Lecture on the Cauchy problem in linear partial differential equations. Yale University Press, New Haven, CT.
14. Hämäläinen, M. S. and Ilmoniemi, R. J. (1994). Interpreting magnetic fields of the brain: minimum norm estimates. Med. Biol. Eng. Comput. 32, 35-42.
15. Hansen, P. C. (1992). Analysis of discrete III-posed problems by means of the L-Curve. SIAM Rev. 34, 561-580.
16. Hoerl, A. E. and Kennard, R. W. (2000). Ridge Regression: biased estimation for nonorthogonal problems. Technometrics 42, 80-86.
17. Hunter, D. R. and Lange, K. (2004). A tutorial on MM algorithms. Amer. Statist. 58, 30-37.
18. Hunter, D. R. and Li, R. (2005). Variable selection using MM algorithms. Ann. Statist. 33, 1617-1642.
19. Kiiveri, H. (2003). A Bayesian approach to variable selection when the number of variables is very large. In Science and Statistics: Festschrift for Terry Speed (Edited by D. R. Goldstein). Institute of Mathematical Statistics Lecture Note-Monograph Series. 40, 127-143.
20. Land, S. and Friedman, J. (1996). Variable fusion: a new method of adaptive signal regression. Technical Report. Department of Statistics, Stanford University, Stanford.
21. Makeig, S., Westerfield, M., Jung, T.-P., Enghoff, S., Townsend, J., Courchesne, E. and Sejnowskii, T. J. (2002). Dynamic brain sources of visual evoked responses. Science. 295, 690-694.
22. Nagarajan, S. S., Portniaguine, O., Hwang, D., Johnson, C. and Sekihara, K. (2006). Controlled support MEG imaging. NeuroImage 33. 878-885.
23. Pascual-Marqui, R. D., Michel, C. M. and Lehmann, D. (1994). Low resolution electromagnetic tomography: a new method for localizing electrical activity in the brain. Int. J. Psychophysiol, 18, 49-65.
24. Pascual-Marqui, R. D. (1999). Review of methods for solving the EEG inverse problem. Inter J. Bioelectromagnetism. 1, 75-86.
25. Pascual-Marqui, R. D., Esslen, M., Kochi, K. and Lehmann, D. (2002). Functional imaging with low-resolution brain electromagnetic tomography (LORETA): A review. Method Find. Exp. Clin. 24, 91-95.
26. Riera, J. J. and Fuentes, M. E. (1998). Electric lead field for a piecewise homogeneous volume conductor model of the head. IEEE Trans. Biomed. Eng. 45, 746-753.
27. Scherg, M. and von Cramon, D. (1986). Evoked dipole source potentials of the human auditory cortex. Electroen. Clin. Neuro. 65, 344-360.
28. Scholz, B. and Schwierz, G. (1994). Probability-based current dipole localization from biomagnetic fields. IEEE T. Bio-Med. Eng. 41, 735-742.
29. Tibshirani, R. (1996). Regression shrinkage and selection via the LASSO. J. Roy. Statist. Soc. Ser. B 58, 267-288.
30. Tibshirani, R., Saunders, M., Rosset, S., Zhu, J. and Knight, K. (2005). Sparsity and smoothness via the fused lasso. J. Roy. Statist. Soc. Ser. B 67, 91-108.
31. Trujillo-Barreto, N., Aubert-Vázquez, E. and Valdés-Sosa, P. A. (2004). Bayesian model averaging in EEG/MEG imaging. Neurolmage. 21, 1300-1319.
32. Valdés-Sosa, P., Marti, F., Garcia, F. and Casanova, R. (2000). Variable resolution electricmagnetic tomographyBiomag 96. Proc. of the Tenth International Conference on Biomagnetism, II, 373-376, Springer-Verlag, New York.
33. Valdés-Sosa, P. A., Sánchez-Bornot, J. M., Vega-Hernández, M., Melie-García, L., Lage- Castellanos, A. and Canales-Rodríguez, E. (2006). Granger Causality on Spatial Manifolds: Applications to Neuroimaging. Handbook of Time Series Analysis: Recent Theoretical Developments and Applications, chapter 18. ISBN: 3-527-40623-9.
34. Vidakovic, B. (1998). Wavelet-Based Nonparametric Bayes Methods. In Practical Nonparametric and Semiparametric Bayesian Statistics (Edited by D. Dey, P. Muller and D. Sinha), 133-156, Springer-Verlag, New York.
35. Yamashita, O., Galka, A., Ozaki, T., Biscay, R. and Valdés-Sosa, P. A. (2004). Recursive penalized least squares solution for the dynamical inverse problem of EEG generation. Hum. Brain Mapp. 21, 221-235.
36. Zou, H. and Hastie, T. (2005). Regularization and variable selection via the elastic net. J. Roy. Statist. Soc. Ser. B 67, 301.