Joint Learning of Full-structure Noise in Hierarchical Bayesian Regression Models

We consider the reconstruction of brain activity from electroencephalography (EEG). This inverse problem can be formulated as a linear regression with independent Gaussian scale mixture priors for both the source and noise components. Crucial factors influencing the accuracy of the source estimation...

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Veröffentlicht in:IEEE transactions on medical imaging Jg. 43; H. 2; S. 1
Hauptverfasser: Hashemi, Ali, Cai, Chang, Gao, Yijing, Ghosh, Sanjay, Muller, Klaus-Robert, Nagarajan, Srikantan S., Haufe, Stefan
Format: Journal Article
Sprache:Englisch
Veröffentlicht: United States IEEE 01.02.2024
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Algorithms
Bayes methods
Bayes Theorem
Bayesian analysis
Brain modeling
Computer Simulation
Covariance matrices
Covariance matrix
EEG
EEG/MEG Brain Source Imaging
Electroencephalography
Electroencephalography - methods
Gaussian noise
Hierarchical Bayesian Learning
Imaging
Inverse problems
Machine learning
Magnetoencephalography - methods
Majorization Minimization
Manifolds
Mathematical models
Noise levels
Observational learning
Random noise
Regression analysis
Regression models
Sparse Bayesian Learning
Type-II Maximum-Likelihood
ISSN:0278-0062, 1558-254X, 1558-254X
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Zusammenfassung:We consider the reconstruction of brain activity from electroencephalography (EEG). This inverse problem can be formulated as a linear regression with independent Gaussian scale mixture priors for both the source and noise components. Crucial factors influencing the accuracy of the source estimation are not only the noise level but also its correlation structure, but existing approaches have not addressed the estimation of noise covariance matrices with full structure. To address this shortcoming, we develop hierarchical Bayesian (type-II maximum likelihood) models for observations with latent variables for source and noise, which are estimated jointly from data. As an extension to classical sparse Bayesian learning (SBL), where across-sensor observations are assumed to be independent and identically distributed, we consider Gaussian noise with full covariance structure. Using the majorization-maximization framework and Riemannian geometry, we derive an efficient algorithm for updating the noise covariance along the manifold of positive definite matrices. We demonstrate that our algorithm has guaranteed and fast convergence and validate it in simulations and with real MEG data. Our results demonstrate that the novel framework significantly improves upon state-of-the-art techniques in the real-world scenario where the noise is indeed non-diagonal and fullstructured. Our method has applications in many domains beyond biomagnetic inverse problems.
Bibliographie:ObjectType-Article-1
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hashemi@tu-berlin.de. sri@ucsf.edu. klausrobert.mueller@tu-berlin.de. haufe@tuberlin.de.
ISSN:0278-0062
1558-254X
1558-254X
DOI:10.1109/TMI.2022.3224085