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

Hashemi, Ali; Cai, Chang; Gao, Yijing; Ghosh, S. K.; Müller, Klaus‐Robert; Nagarajan, Srikantan S.; Haufe, Stefan

doi:10.1109/tmi.2022.3224085

Cited by 11 publications

(4 citation statements)

References 62 publications

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“…In this paper, we choose noise-learned Champagne [Cai et al 2021] as the key benchmarks to compare with. Two other we compare are sLORETA [7] and full structure noise (FUN) learning method [16]. The performance of simulated brain source reconstruction is evaluated based on response receiver operator characteristics (FROC) [12].…”

Section: Resultsmentioning

confidence: 99%

Bayesian Inference for Brain Source Imaging with Joint Estimation of Structured Low-rank Noise

Ghosh

Cai

Gao

et al. 2023

Preprint

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The inverse problem in brain source imaging is the reconstruction of brain activity from non-invasive recordings of electroencephalography (EEG) and magnetoencephalography (MEG). One key challenge is the efficient recovery of sparse brain activity when the data is corrupted by structured noise that is low-rank noise. This is often the case when there are a few active sources of environmental noise and the MEG/EEG sensor noise is highly correlated. In this paper, we propose a novel robust empirical Bayesian framework which provides us a tractable algorithm for jointly estimating a low-rank noise covariance and brain source activity. Specifically, we use a factor analysis model for the structured noise, and infer a sparse set of variance parameters for source activity, while performing variational Bayesian inference for the noise. One key aspect of this algorithm is that it does not require any additional baseline measurements to estimate the noise covariance from the sensor data. We perform exhaustive experiments on both simulated and real datasets. Our algorithm achieves superior performance as compared to several existing benchmark algorithms.

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Section: Resultsmentioning

confidence: 99%

Bayesian Inference for Brain Source Imaging with Joint Estimation of Structured Low-rank Noise

Ghosh

Cai

Gao

et al. 2023

Preprint

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“…While being broadly applicable (see [64, Appendix A] for a comprehensive list of potential applications), our approach is nevertheless limited by a number of factors. Although Gaussian noise distributions are commonly justified, it would be interesting to include more robust non-Gaussian noise distributions in our framework.…”

Section: Discussionmentioning

confidence: 99%

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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“…One such method is sparse Bayesian learning (SBL) [21], [22]. Under the SBL framework, the study in [23] combines the hyperparameters of the source variance along with the full-structure multivariate Gaussian noise for joint estimation, leading to promising outcomes. Cai et al [24] utilize SBL to estimate the model data covariance and reconstruct potential sources with adaptive beamformers, effectively mitigating the effects of correlated brain sources and yielding good results.…”

Section: Introductionmentioning

confidence: 99%

VSSI-GGD: A Variation Sparse EEG Source Imaging Approach Based on Generalized Gaussian Distribution

Liu,

Peng,

Liang

et al. 2024

IEEE Trans. Neural Syst. Rehabil. Eng.

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Electroencephalographic (EEG) source imaging (ESI) is a powerful method for studying brain functions and surgical resection of epileptic foci. However, accurately estimating the location and extent of brain sources remains challenging due to noise and background interference in EEG signals. To reconstruct extended brain sources, we propose a new ESI method called Variation Sparse Source Imaging based on Generalized Gaussian Distribution (VSSI-GGD). VSSI-GGD uses the generalized Gaussian prior as a sparse constraint on the spatial variation domain and embeds it into the Bayesian framework for source estimation. Using a variational technique, we approximate the intractable true posterior with a Gaussian density. Through convex analysis, the Bayesian inference problem is transformed entirely into a series of regularized L 2p -norm (0 < p < 1) optimization problems, which are efficiently solved with the ADMM algorithm. Imaging results of numerical simulations and human experimental dataset analysis reveal the superior performance of VSSI-GGD, which provides higher spatial resolution with clear boundaries compared to benchmark algorithms. VSSI-GGD can potentially serve as an effective and robust spatiotemporal EEG source imaging method. The source code of VSSI-GGD is available at https://github.com/Mashirops/VSSI-GGD.git.

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

Cited by 11 publications

References 62 publications

Bayesian Inference for Brain Source Imaging with Joint Estimation of Structured Low-rank Noise

Bayesian Inference for Brain Source Imaging with Joint Estimation of Structured Low-rank Noise

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

VSSI-GGD: A Variation Sparse EEG Source Imaging Approach Based on Generalized Gaussian Distribution

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