Prior Variances and Depth Un-Biased Estimators in EEG Focal Source Imaging

  • A. Koulouri
  • V. Rimpiläinen
  • M. Brookes
  • J. P. Kaipio
Conference paper
Part of the IFMBE Proceedings book series (IFMBE, volume 65)

Abstract

In electroencephalography (EEG) source imaging, the inverse source estimates are depth biased in such a way that their maxima are often close to the sensors. This depth bias can be quantified by inspecting the statistics (mean and covariance) of these estimates. In this paper, we find weighting factors within a Bayesian framework for the used \(\ell _1/\ell _2\) sparsity prior that the resulting maximum a posterior (MAP) estimates do not favour any particular source location. Due to the lack of an analytical expression for the MAP estimate when this sparsity prior is used, we solve the weights indirectly. First, we calculate the Gaussian prior variances that lead to depth un-biased maximum a posterior (MAP) estimates. Subsequently, we approximate the corresponding weight factors in the sparsity prior based on the solved Gaussian prior variances. Finally, we reconstruct focal source configurations using the sparsity prior with the proposed weights and two other commonly used choices of weights that can be found in literature.

Keywords

Electroencephalography sparsity prior Gaussian prior Bayesian inverse problems depth bias 

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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • A. Koulouri
    • 1
  • V. Rimpiläinen
    • 2
  • M. Brookes
    • 3
  • J. P. Kaipio
    • 4
  1. 1.Institute for Computational and Applied Mathematics, University of MünsterMünsterGermany
  2. 2.Institute for Biomagnetism and Biosignalanalysis, University of MünsterMünsterGermany
  3. 3.Department of Electrical and Electronic Engineering, Imperial College LondonLondonUK
  4. 4.Department of Mathematics, University of AucklandAucklandNew Zealand

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