Penalized Least Squares methods for solving the EEG Inverse Problem

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

Research output: Contribution to journalArticle

32 Citations (Scopus)

Abstract

Most of the known solutions (linear and nonlinear) of the ill-posed EEG Inverse Problem can be interpreted as the estimated coefficients in a penalized regression framework. In this work we present a general formulation of this problem as a Multiple Penalized Least Squares model, which encompasses many of the previously known methods as particular cases (e.g., Minimum Norm, LORETA). New types of inverse solutions arise since recent advances in the field of penalized regression have made it possible to deal with non-convex penalty functions, which provide sparse solutions (Fan and Li (2001)). Moreover, a generalization of this approach allows the use of any combination of penalties based on 11 or 12-norms, leading to solutions with combined properties such as smoothness and sparsity. Synthetic data is used to explore the benefits of non-convex penalty functions (e.g., LASSO, SCAD and LASSO Fusion) and mixtures (e.g., Elastic Net and LASSO Fused) by comparing them with known solutions in terms of localization error, blurring and visibility. Real data is used to show that a mixture model (Elastic Net) allows for tuning the spatial resolution of the solution to range from very concentrated to very blurred sources.

LanguageEnglish
Pages1535-1551
Number of pages17
JournalStatistica Sinica
Volume18
Issue number4
Publication statusPublished - 1 Oct 2008

Fingerprint

Elastic Net
Penalized Regression
Penalized Least Squares
Penalty Function
Least Square Method
Inverse Problem
Norm
Synthetic Data
Mixture Model
Visibility
Sparsity
Spatial Resolution
Penalty
Smoothness
Tuning
Fusion
Formulation
Coefficient
Range of data
Electroencephalogram

Keywords

  • EEG
  • Inverse Problem
  • Least Squares
  • Penalized regression

Cite this

Vega-Hernández, M., Martínez-Montes, E., Sánchez-Bornot, J. M., Lage-Castellanos, A., & Valdés-Sosa, P. A. (2008). Penalized Least Squares methods for solving the EEG Inverse Problem. Statistica Sinica, 18(4), 1535-1551.
Vega-Hernández, Mayrim ; Martínez-Montes, Eduardo ; Sánchez-Bornot, José M. ; Lage-Castellanos, Agustín ; Valdés-Sosa, Pedro A. / Penalized Least Squares methods for solving the EEG Inverse Problem. In: Statistica Sinica. 2008 ; Vol. 18, No. 4. pp. 1535-1551.
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Vega-Hernández, M, Martínez-Montes, E, Sánchez-Bornot, JM, Lage-Castellanos, A & Valdés-Sosa, PA 2008, 'Penalized Least Squares methods for solving the EEG Inverse Problem', Statistica Sinica, vol. 18, no. 4, pp. 1535-1551.

Penalized Least Squares methods for solving the EEG Inverse Problem. / Vega-Hernández, Mayrim; Martínez-Montes, Eduardo; Sánchez-Bornot, José M.; Lage-Castellanos, Agustín; Valdés-Sosa, Pedro A.

In: Statistica Sinica, Vol. 18, No. 4, 01.10.2008, p. 1535-1551.

Research output: Contribution to journalArticle

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Vega-Hernández M, Martínez-Montes E, Sánchez-Bornot JM, Lage-Castellanos A, Valdés-Sosa PA. Penalized Least Squares methods for solving the EEG Inverse Problem. Statistica Sinica. 2008 Oct 1;18(4):1535-1551.