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Unification of sparse Bayesian learning algorithms for electromagnetic brain imaging with the majorization

Ali Hashemi1, Chang Cai2, Gitta Kutyniok3

  • 1Uncertainty, Inverse Modeling and Machine Learning Group, Technische Universität Berlin, Germany; Machine Learning Group, Technische Universität Berlin, Germany; Berlin Center for Advanced Neuroimaging (BCAN), Charité - Universitätsmedizin Berlin, Germany; Institut für Mathematik, Technische Universität Berlin, Germany.

Neuroimage
|June 28, 2021
PubMed
Summary

Sparse Bayesian learning (SBL) for electroencephalography/magnetoencephalography (EEG/MEG) brain source imaging is improved with a new method (LowSNR-BSI) for low signal-to-noise ratios and accurate noise level estimation.

Keywords:
Brain source imagingElectro-/magnetoencephalographyHyperparameter learningMajorization-MinimizationNoise learningNon-convexType I/II Bayesian learning

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Area of Science:

  • Neuroscience
  • Signal Processing
  • Computational Biology

Background:

  • Sparse Bayesian learning (SBL) is effective for brain source imaging (BSI) with electroencephalography (EEG) and magnetoencephalography (MEG), particularly for event-related designs with few active sources.
  • Accurate source reconstruction in BSI relies heavily on precise knowledge of noise levels.

Purpose of the Study:

  • To enhance SBL algorithms for BSI by unifying existing methods under the majorization-minimization (MM) framework.
  • To introduce a novel method, LowSNR-BSI, for improved source reconstruction in low signal-to-noise ratio (SNR) conditions.
  • To develop a principled technique for accurate noise variance estimation directly from BSI data.

Main Methods:

  • Reformulated three existing SBL algorithms within the majorization-minimization (MM) framework for theoretical unification and novel algorithm development.
  • Proposed LowSNR-BSI, a novel MM-based method optimized for low SNR environments.
  • Developed a new technique for learning noise variance from data, either jointly or via cross-validation, improving upon baseline estimates.

Main Results:

  • Monotonous convergence behavior of MM-based SBL algorithms was empirically confirmed.
  • LowSNR-BSI demonstrated superior source reconstruction performance in low SNR regimes compared to conventional SBL.
  • Learned noise levels significantly outperformed estimates derived from baseline data in accuracy.

Conclusions:

  • The MM framework provides a unified perspective for SBL algorithm development in BSI.
  • The proposed LowSNR-BSI method and data-driven noise variance estimation significantly advance BSI capabilities, especially in challenging low SNR conditions.
  • Neurophysiologically plausible source reconstructions were achieved on auditory evoked potential data, validating the practical utility of the novel approach.