The global signal is widely used as a regressor or normalization factor for removing the effects of global variations in the analysis of functional magnetic resonance imaging (fMRI) studies. However, there is considerable controversy over its use because of the potential bias that can be introduced when it is applied to the analysis of both task-related and resting-state fMRI studies. In this paper we take a closer look at the global signal, examining in detail the various sources that can contribute to the signal. For the most part, the global signal has been treated as a nuisance term, but there is growing evidence that it may also contain valuable information. We also examine the various ways that the global signal has been used in the analysis of fMRI data, including global signal regression, global signal subtraction, and global signal normalization. Furthermore, we describe new ways for understanding the effects of global signal regression and its relation to the other approaches.

In resting-state functional MRI (rsfMRI), the correlation between blood oxygenation level dependent (BOLD) signals across different brain regions is used to estimate the functional connectivity of the brain. This approach has led to the identification of a number of resting-state networks, including the default mode network (DMN) and the task positive network (TPN). Global signal regression (GSR) is a widely used pre-processing step in rsfMRI that has been shown to improve the spatial specificity of the estimated resting-state networks. In GSR, a whole brain average time series, known as the global signal (GS), is regressed out of each voxel time series prior to the computation of the correlations. However, the use of GSR is controversial because it can introduce artifactual negative correlations. For example, it has been argued that anticorrelations observed between the DMN and TPN are primarily an artifact of GSR. Despite the concerns about GSR, there is currently no consensus regarding its use. In this paper, we introduce a new framework for understanding the effects of GSR. In particular, we show that the main effects of GSR can be well approximated as a temporal downweighting process in which the data from time points with relatively large GS magnitudes are greatly attenuated while data from time points with relatively small GS magnitudes are largely unaffected. Furthermore, we show that a limiting case of this downweighting process in which data from time points with large GS magnitudes are censored can also approximate the effects of GSR. In other words, the correlation maps obtained after GSR show a high degree of spatial similarity (including the presence of anticorrelations between the DMN and TPN) with maps obtained using only the uncensored (i.e. retained) time points. Since the data from these retained time points are unaffected by the censoring process, this finding suggests that the observed anticorrelations inherently exist in the data from time points with small GS magnitudes and are not simply an artifact of GSR.

In resting-state fMRI, dynamic functional connectivity (DFC) measures are used to characterize temporal changes in the brain's intrinsic functional connectivity. A widely used approach for DFC estimation is the computation of the sliding window correlation between blood oxygenation level dependent (BOLD) signals from different brain regions. Although the source of temporal fluctuations in DFC estimates remains largely unknown, there is growing evidence that they may reflect dynamic shifts between functional brain networks. At the same time, recent findings suggest that DFC estimates might be prone to the influence of nuisance factors such as the physiological modulation of the BOLD signal. Therefore, nuisance regression is used in many DFC studies to regress out the effects of nuisance terms prior to the computation of DFC estimates. In this work we examined the relationship between seed-specific sliding window correlation-based DFC estimates and nuisance factors. We found that DFC estimates were significantly correlated with temporal fluctuations in the magnitude (norm) of various nuisance regressors. Strong correlations between the DFC estimates and nuisance regressor norms were found even when the underlying correlations between the nuisance and fMRI time courses were relatively small. We then show that nuisance regression does not necessarily eliminate the relationship between DFC estimates and nuisance norms, with significant correlations observed between the DFC estimates and nuisance norms even after nuisance regression. We present theoretical bounds on the difference between DFC estimates obtained before and after nuisance regression and relate these bounds to limitations in the efficacy of nuisance regression with regards to DFC estimates.

In resting-state fMRI, dynamic functional connectivity (DFC) measures are used to characterize temporal changes in the brain's intrinsic functional connectivity. A widely used approach for DFC estimation is the computation of the sliding window correlation between blood oxygenation level dependent (BOLD) signals from di↵erent brain regions. Although the source of temporal fluctuations in DFC estimates remains largely unknown, there is growing evidence that they may reflect dynamic shifts between functional brain networks. At the same time, recent findings suggest that DFC estimates might be prone to the influence of nuisance factors such as the physiological modulation of the BOLD signal. Therefore, nuisance regression is used in many DFC studies to regress out the e↵ects of nuisance terms prior to the computation of DFC estimates. In this work we examined the relationship between DFC estimates and nuisance factors.We found that DFC estimates were significantly correlated with temporal fluctuations in the magnitude (norm) of various nuisance regressors, with significant correlations observed in the majority (76%) of the cases examined. Significant correlations between the DFC estimates and nuisance regressor norms were found even when the underlying correlations between the nuisance and fMRI time courses were relatively small. We then show that nuisance regression does not eliminate the relationship between DFC estimates and nuisance norms, with significant correlations observed in the majority (71%) of the cases examined after nuisance regression. We present theoretical bounds on the di↵erence between DFC estimates obtained before and after nuisance regression and relate these bounds to limitations in the ⇤ Corresponding Author ⇤⇤ Principal Corresponding Author Email addresses: analci@ucsd.edu (Alican Nalci), ttliu@ucsd.edu (Thomas T. Liu). CC-BY-NC-ND 4.0 International license It is made available under a (which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity.The copyright holder for this preprint . http://dx.doi.org/10.1101/285239 doi: bioRxiv preprint first posted online Mar. 21, 2018; e cacy of nuisance regression with regards to DFC estimates.

In this paper, we develop a Bayesian evidence maximization framework to solve the sparse non-negative least squares (S-NNLS) problem. We introduce a family of probability densities referred to as the Rectified Gaussian Scale Mixture (R-GSM) to model the sparsity enforcing prior distribution for the solution. The R-GSM prior encompasses a variety of heavy-tailed densities such as the rectified Laplacian and rectified Studentt distributions with a proper choice of the mixing density. We utilize the hierarchical representation induced by the R-GSM prior and develop an evidence maximization framework based on the Expectation-Maximization (EM) algorithm. Using the EM based method, we estimate the hyper-parameters and obtain a point estimate for the solution. We refer to the proposed method as rectified sparse Bayesian learning (R-SBL). We provide four R-SBL variants that offer a range of options for computational complexity and the quality of the E-step computation. These methods include the Markov chain Monte Carlo EM, linear minimum mean-square-error estimation, approximate message passing and a diagonal approximation. Using numerical experiments, we show that the proposed R-SBL method outperforms existing S-NNLS solvers in terms of both signal and support recovery performance, and is also very robust against the structure of the design matrix.