Unification of Sparse Bayesian Learning Algorithms for Electromagnetic Brain Imaging with the Majorization Minimization Framework

Hashemi, Ali; Cai, Chang; Kutyniok, Gitta; Müller, Klaus‐Robert; Hinkley, Leighton B.; Haufe, Stefan

doi:10.1101/2020.08.10.243774

Cited by 3 publications

(1 citation statement)

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“…The voxel variance hyperparameters are estimated by maximizing a bound on the marginal likelihood p ( Y | α ). Although there are multiple ways to derive update rules for α ( Wipf and Nagarajan, 2009 ), in Champagne we utilize a convex bounding ( Jordan et al, 1999 ) on the logarithm of marginal likelihood (model evidence), which results in fast and convergent update rules ( Hashemi et al, 2020 ). For a detailed derivation of the original Champagne, we refer to our previous paper ( Wipf et al, 2010 ).…”

Section: Methodsmentioning

confidence: 99%

Robust estimation of noise for electromagnetic brain imaging with the champagne algorithm

et al. 2021

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Robust estimation of the number, location, and activity of multiple correlated brain sources has long been a challenging task in electromagnetic brain imaging from M/EEG data, one that is significantly impacted by interference from spontaneous brain activity, sensor noise, and other sources of artifacts. Recently, we introduced the Champagne algorithm, a novel Bayesian inference algorithm that has shown tremendous success in M/EEG source reconstruction. Inherent to Champagne and most other related Bayesian reconstruction algorithms is the assumption that the noise covariance in sensor data can be estimated from “baseline” or “control” measurements. However, in many scenarios, such baseline data is not available, or is unreliable, and it is unclear how best to estimate the noise covariance. In this technical note, we propose several robust methods to estimate the contributions to sensors from noise arising from outside the brain without the need for additional baseline measurements. The incorporation of these methods for diagonal noise covariance estimation improves the robust reconstruction of complex brain source activity under high levels of noise and interference, while maintaining the performance features of Champagne. Specifically, we show that the resulting algorithm, Champagne with noise learning, is quite robust to initialization and is computationally efficient. In simulations, performance of the proposed noise learning algorithm is consistently superior to Champagne without noise learning. We also demonstrate that, even without the use of any baseline data, Champagne with noise learning is able to reconstruct complex brain activity with just a few trials or even a single trial, demonstrating significant improvements in source reconstruction for electromagnetic brain imaging.

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Section: Methodsmentioning

confidence: 99%

Robust estimation of noise for electromagnetic brain imaging with the champagne algorithm

et al. 2021

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

Hashemi

Cai

Gao

et al. 2021

Preprint

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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 accuracy of source estimation are not only the noise level but also its correlation structure, but existing approaches have not addressed 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 fully-structured. Our method has applications in many domains beyond biomagnetic inverse problems.

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Identifying good practices for detecting inter-regional linear functional connectivity from EEG

Pellegrini

Delorme

Nikulin

et al. 2022

Preprint

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Aggregating voxel-level statistical dependencies between multivariate time series is an important intermediate step when characterising functional connectivity (FC) between larger brain regions. However, there are numerous ways in which voxel-level data can be aggregated into inter-regional FC, and the advantages of each of these approaches are currently unclear. In this study we generate ground-truth data and compare the performances of various pipelines that estimate directed and undirected linear FC between regions. We test the ability of several existing and novel FC analysis pipelines to identify the true regions within which connectivity was simulated. We test various inverse modelling algorithms, strategies to aggregate time series within regions, and connectivity metrics. Furthermore, we investigate the influence of the number of interactions, the signal-to-noise ratio, the noise mix, the interaction time delay, and the number of active sources per region on the ability of detecting FC. The best-performing FC pipeline consists of the following steps: (1) Source projection using the linearly-constrained minimum variance (LCMV) beamformer. (2) Principal component analysis (PCA) using the same fixed number of components within every region. (3) Calculation of the multivariate interaction measure (MIM) for every region pair to assess undirected FC, or calculation of time-reversed Granger Causality (TRGC) to assess directed FC. Lowest performance is obtained with pipelines involving the absolute value of coherency. Interestingly, the combination of dynamic imaging of coherent sources (DICS) beamforming with directed FC metrics that aggregate information across multiple frequencies leads to unsatisfactory results. We formulate recommendations based on these results that may increase the validity of future experimental connectivity studies. We further introduce the free ROIconnect plugin for the EEGLAB toolbox that includes the recommended methods and pipelines that are presented here. We show an exemplary application of the best performing pipeline to the analysis EEG data recorded during motor imagery.

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Unification of Sparse Bayesian Learning Algorithms for Electromagnetic Brain Imaging with the Majorization Minimization Framework

Cited by 3 publications

References 121 publications

Robust estimation of noise for electromagnetic brain imaging with the champagne algorithm

Robust estimation of noise for electromagnetic brain imaging with the champagne algorithm

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

Identifying good practices for detecting inter-regional linear functional connectivity from EEG

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