Jump to : Download | Abstract | Keywords | Contact | BibTex reference | EndNote reference |

PRF02b

C. Phillips, M. D. Rugg, K. J. Friston. Systematic regularization of linear inverse solutions of the EEG source localization problem. NeuroImage, 17(1):287-301, 2002.

Download

Download paper: (link)

Copyright notice:This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. These works may not be reposted without the explicit permission of the copyright holder.

Abstract

Distributed linear solutions of the EEG source localization problem are used routinely. Here we describe an approach based on the weighted minimum norm method that imposes constraints using anatomical and physiological information derived from other imaging modalities to regularize the solution. In this approach the hyperparameters controlling the degree of regularization are estimated using restricted maximum likelihood (ReML). EEG data are always contaminated by noise, e.g., exogenous noise and background brain activity. The conditional expectation of the source distribution, given the data, is attained by carefully balancing the minimization of the residuals induced by noise and the improbability of the estimates as determined by their priors. This balance is specified by hyperparameters that control the relative importance of fitting and conforming to prior constraints. Here we introduce a systematic approach to this regularization problem, in the context of a linear observation model we have described previously. In this model, basis functions are extracted to reduce the solution space a priori in the spatial and temporal domains. The basis sets are motivated by knowledge of the evoked EEG response and information theory. In this paper we focus on an iterative "expectation-maximization" procedure to jointly estimate the conditional expectation of the source distribution and the ReML hyperparameters on which this solution rests. We used simulated data mixed with real EEG noise to explore the behavior of the approach with various source locations, priors, and noise levels. The results enabled us to conclude: (i) Solutions in the space of informed basis functions have a high face and construct validity, in relation to conventional analyses. (ii) The hyperparameters controlling the degree of regularization vary largely with source geometry and noise. The second conclusion speaks to the usefulness of using adaptative ReML hyperparameter estimates

Keywords

[ *algorithms ] [ Bayes theorem ] [ Brain/anatomy & histology/physiology ] [ Electroencephalography/*statistics & numerical data ] [ Electromagnetic fields ] [ Head/anatomy & histology ] [ Linear models ] [ Models ] [ Anatomic ]

Contact

C. Phillips
M. D. Rugg
K. J. Friston

BibTex Reference

@article{PRF02b,
   Author = {Phillips, C. and Rugg, M. D. and Friston, K. J.},
   Title = {Systematic regularization of linear inverse solutions of the {EEG} source localization problem},
   Journal = {NeuroImage},
   Volume = {17},
   Number = {1},
   Pages = {287--301},
   Year = {2002}
}

EndNote Reference [help]

Get EndNote Reference (.ref)