Structured Noise Champagne: An Empirical Bayesian Algorithm for Electromagnetic Brain Imaging With Structured Noise

Sanjay Ghosh ¹ Chang Cai ² Ali Hashemi ³ Yijing Gao ¹ Stefan Haufe ³ Kensuke Sekihara ⁴ Ashish Raj ¹ Srikantan S Nagarajan ^1*

• ¹ Biomagnetic Imaging Lab, Department of Radiology and Biomedical Imaging, University of California San Francisco, San Francisco, United States
• ² Central China Normal University, Wuhan, Hubei Province, China
• ³ Technical University of Berlin, Berlin, Brandenburg, Germany
• ⁴ Signal Analysis Inc., Tokyo, Japan

Electromagnetic brain imaging is the reconstruction of brain activity from non-invasive recordings of electroencephalography (EEG), magnetoencephalography (MEG), and also from invasive ones like the intracranial recording of electrocorticography (ECoG), intracranial (iEEG) and stereo EEG (sEEG). These modalities are widely used techniques to study the function of human brain. Efficient reconstruction of electrophysiological activity of neurons in the brain from EEG/MEG measurements is important for neuroscience research and clinical applications. An enduring challenge in this field is the accurate inference of brain signals of interest while accounting for all sources of noise that contribute to the sensor measurements. The statistical characteristics of the noise plays a crucial role in the success of brain source recovery process which can be formulated as a sparse regression problem. In this work, we assume that dominant environment and biological sources of noise that have high spatial correlations in the sensors can be expressed as a structured noise model based on variational Bayesian factor analysis. To the best of our knowledge, no existing algorithm has addressed the brain source estimation problem with such structured noise. We propose to apply a robust empirical Bayesian framework for iteratively estimating the brain source activity and the statistics of the structured noise. In particular, we perform inference of the variational Bayesian Factor Analysis (VBFA) noise model iteratively in conjunction with source reconstruction. A key aspect of our algorithm is that we do not require any additional baseline measurements to estimate the noise covariance from the sensor data under scenarios like resting-state analysis, and other use cases wherein a noise or artifactual source occurs only in the active period but not in the baseline period (e.g. neuromodulatory stimulation artifacts, speech movements etc. To demonstrate the effectiveness of the proposed algorithm, we perform experiments on both simulated and real datasets. Our algorithm achieves superior performance as compared to several existing benchmark algorithms.