Abstract
Electroencephalographic (EEG) source imaging depends upon sophisticated signal processing algorithms to deal with the problems of data cleaning, source separation, and localization. Typically, these problems are sequentially addressed by independent heuristics, limiting the use of EEG images on a variety of applications. Here, we propose a unifying empirical Bayes framework in which these dissimilar problems can be solved using a single algorithm. We use spatial sparsity constraints to adaptively segregate brain sources into maximally independent components with known anatomical support, while minimally overlapping artifactual activity. The framework yields a recursive inverse spatiotemporal filter that can be used for offline and online applications. We call this filter Recursive Sparse Bayesian Learning (RSBL). Of theoretical relevance, we demonstrate the connections between Infomax Independent Component Analysis and RSBL. We use simulations to show that RSBL can separate and localize cortical and artifact components that overlap in space and time from noisy data. On real data, we use RSBL to analyze single-trial error-related potentials, finding sources in the cingulate gyrus. We further benchmark our algorithm on two unrelated EEG studies showing that: 1) it outperforms Infomax for source separation on short time-scales and 2), unlike the popular Artifact Subspace Removal algorithm, it can reduce artifacts without significantly distorting clean epochs. Finally, we analyze mobile brain/body imaging data to characterize the brain dynamics supporting heading computation during full-body rotations, replicating the main findings of previous experimental literature.
Footnotes
1- We added two sections (2.1.1-2.1.2) to explain how the lead field and artifact dictionaries are obtained. 2- It was pointed out that PEB is the name of a fairly general probabilistic framework so that PEB+ was a bit of abuse of nomenclature. Here we have renamed our algorithm as RSBL (Recursive Sparse Bayesian Learning), which also reflects more accurately the modifications introduced in this version. 3- A major weakness of the previous (instantaneous) approach was that it relied on the iid data assumption used to optimize the evidence of a block of EEG. This assumption was a very very crude approximation of reality because the EEG has short-term auto-correlation. In the current version, we dispense with the iid assumption and introduce a temporal dynamic constraint. This yields a state-space representation of the generative model, which, ideally, could be solved with a Kalman filter (KF). However, we argue that the KF is not feasible in this context (uncertain brain/plant dynamic equation and large dimensional source (state) space), so we propose a simple modification to the KF to make it tractable, which we call Recursive Sparse Bayesian Learning (RSBL). RSBL has the same characteristics of block sparsity as in the previous version of the paper, but now 1) we learn (optimize) the model (sparsity profile of the sources and common-mode sensor noise) on a sample by sample basis and 2) we use a simple neurodynamic model to ensure spatiotemporal smoothness from one sample to the next. These changes are in sections 2.2-2.4. 4- The model comparison figure was hard to read, and it stated the obvious, source estimation benefits from joint artifact modeling. We have removed that section to get more room for the new material. 5- We test our algorithm on simulated data in Section 3.2. 6- We test our algorithm on real error-related potential ERP data in Sections 3.3-3.4. 7- After re-running the analysis of the MoBI section, the ERSP result remains virtually unchanged, at least to the naked eye. This is expected because 1) the core of the algorithm remains the same and 2) after the source time series in the RSC region is computed we calculate its time-frequency decomposition of it, which has the effect of significantly smoothing the ERSP, which may have washed out subtle details that we may have picked up with this version of the algorithm.