Robust Estimation of Noise for Electromagnetic Brain Imaging with the Champagne Algorithm

Abstract

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 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.

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

“…Note that the superior spatial reconstruction of sparsity-inducing algorithms (Champagne, LowSNR-BSI and S-FLEX) compared to eLORETA is expected here, because the simulated spatial distributions are indeed sparse. The superiority of SBL methods (Champagne, LowSNR-BSI) over S-FLEX that is observed here confirms observations and theoretical considerations made in [6], [23], [24]. eLORETA shows comparable temporal reconstruction performance as LowSNR-BSI and Champagne, while S-FLEX is outperformed by all other methods.…”

“…In contrast, the computational complexity of the proposed noise level estimation scheme using adaptive learning is of the same order as the complexity of the baseline approach. Moreover, we have successfully extended this approach to the estimation of heteroscedastic noise, where a distinct variance is estimated for each M/EEG sensor [24]. Hence, the adaptive-learning approach can be seen as an advancement of the baseline algorithm that combines performance improvement and computational efficiency.…”

“…On the other hand, modeling dependency structures that are in fact present in real data has the potential to substantially improve the source reconstruction. We have recently proposed adaptive noise learning algorithms that relax the rather unrealistic assumption of homoscedastic noise [24]. Going further, it would be possible to also model spatial covariances of the sources between voxels and/or between source orientation within voxels, which would encode the realistic assumption that individual brain regions do not work in isolation.…”

“…The prestimulus window was selected to be –100 ms to 5 ms and the post-stimulus time window was selected to be 5 ms to 250 ms, where 0 ms is the onset of the tone. Further details on this dataset can be found in [23], [24], [78]. The lead field for each subject was calculated with NUTMEG (http://bil.ucsf.edu) using a single-sphere head model (two spherical orientation lead fields) and an 8 mm voxel grid.…”

“…This holds in particular for the reconstruction of ongoing as well as induced (non-phase-locked) oscillatory activity, where no averaging can be performed prior to source reconstruction. Current SBL algorithms may suffer from reduced performance in such low-SNR regimes [22]–[24]. To overcome this limitation, we propose a novel MM algorithm for EEG/MEG source imaging, which employs a bound on the SBL cost function that is particularly suitable for low-SNR regimes.…”