Model based fMRI denoising

Poster No:


Submission Type:

Abstract Submission 


Luigi Gresele1, Klaus Scheffler2, Bernhard Schölkopf3, Gabriele Lohmann4


1Max-Planck Institute for Intelligent Systems, Max-Planck Institute for Biological Cybernetics, Tübingen, Germany, 2Max-Planck Institute for Biological Cybernetics, University of Tübingen, Tübingen, Germany, 3Max-Planck Institute for Intelligent Systems, Tübingen, Germany, 4Max-Planck Institute for Biological Cybernetics, Tübingen, Germany


Denoising functional magnetic resonance imaging (fMRI) data amounts to extracting the component which is informative about localized brain activity, removing the multiple confounding effects intervening during the acquisition process. Data driven methods (i.e., without additional information coming from external measurements) for disentangling signal and noise are generally presented without discussing the mechanism generating the observations as a composition of the two. In some cases, it is even unclear which nuisance source is being targeted. While blindness to the data generating process may be regarded as appealing, since it makes the specification of a noise model unnecessary, complete ignorance about it may result in application of inappropriate procedures, which could either destroy some of the signal of interest, or fail in retrieving it.
In order to make denoising more principled, we simultaneously try to model how noise and signal are mixed in our observations, and understand whether the commonly used methods have the required properties to achieve the desired disentanglement and retrieve the signal.


We classify different functional models of how noise and signal jointly give rise to observations, leveraging the taxonomy developed in the field of causal modelling; discuss how specific nuisance processes in the data acquisition fit the above taxonomy, focusing mainly on physiological noise and motion artifacts; and identify which methods are to be considered well principled in correcting for different kinds of noise, investigating whether a mismatch between the noise and the denoising models can still permit recovery of the signal.
We report that most of the commonly used methods are limited to an additive noise assumption. Furthermore, most of the data driven approaches can be described as special cases of half-sibling regression (Schölkopf, 2016). This technique, originally developed in the field of causal inference, assumes that both the target voxels and a noise region of interest are affected by the same noise source in an additive manner; builds predictive models from the latter to the former; and subtracts the prediction from the target time series, yielding an estimate of the unconfounded signal.
Supporting Image: noise_models.png
   ·a) Causal graph for signal-noise mixing; b) Functional causal model (FCM) for additive noise; c) Nonlinear additive noise; d) Post-nonlinear noise model (which includes scalar multiplicative noise)


The popular CompCor methods (Behzadi, 2007) are shown to be special cases of half-sibling regression, and the analogy extends to many others. The efficiency and effectiveness metrics used to evaluate denoising strategies (Ciric, 2018) can then be translated into the Machine Learning terminology as overfitting and underfitting, suggesting regularization to improve efficiency; analysis on motor task data from ten subjects (Gordon, 2017) shows higher z-values for a half-sibling regression with a ridge regression model with respect to aCompCor.
We furthermore argue that two motion and physiology related mechanisms (rigid body motion and breathing induced perturbations of the magnetic field) cannot be modeled as additive. We show that assuming noise additivity for data in which the confounding is multiplicative may remove part of the relevant signal and introduce a fictitious time dependent structure in the residuals. We support this claim with analytical computations.
Supporting Image: hsr_brain_ohbm.png
   ·a)Half-sibling regression graph; b) FCM; c) CompCor methods are instances of HSR, with WHM or CSF as noise ROI; d) Task data performance of aCompCor, HSR with ridge and no confound regression (z>3)


The connection between half-sibling regression and the confound regression techniques, modeling nuisance processes as time series, clarifies the underlying assumptions and paves the way for an extension of the confound model class (e.g., exploiting more complex signal-noise mixing, nonlinear predictive models, temporal structure of the data).
We also establish a mapping between the language of fMRI preprocessing and that of Machine Learning and Causal Inference, hoping that this may bridge the two communities, resulting in useful knowledge transfer and clarification of the theoretical properties of the fMRI denoising problems. Effective fMRI preprocessing requires taking into account the data generating mechanisms, in order to develop well suited techniques.

Imaging Methods:



Informatics Other

Modeling and Analysis Methods:

Methods Development 2
Motion Correction and Preprocessing 1


Data analysis
Machine Learning
Statistical Methods
Other - Causal Inference

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My abstract is being submitted as a Software Demonstration.


Please indicate below if your study was a "resting state" or "task-activation” study.


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Was any human subjects research approved by the relevant Institutional Review Board or ethics panel? NOTE: Any human subjects studies without IRB approval will be automatically rejected.

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Please indicate which methods were used in your research:

Functional MRI

Provide references using author date format

Behzadi, Y. (2007), 'A component based noise correction method (CompCor) for BOLD and perfusion based fMRI', Neuroimage, 37(1), 90-101.
Brosch, J. R. (2002), 'Simulation of human respiration in fMRI with a mechanical model', IEEE Transactions on Biomedical Engineering, 49(7), 700-707.
Ciric, R. (2018), 'Mitigating head motion artifact in functional connectivity MRI', Nature protocols, 1.
Esteban, O. (2018), 'FMRIPrep: a robust preprocessing pipeline for functional MRI', bioRxiv. DOI, 10, 306951.
Gordon, E. M. (2017), 'Precision functional mapping of individual human brains', Neuron, 95(4), 791-807.
Liu, T. T. (2016), 'Noise contributions to the fMRI signal: An overview', NeuroImage, 143, 141-151.
Peters, J. (2017), 'Elements of causal inference: foundations and learning algorithms', MIT press.
Schölkopf, B. (2016), 'Modeling confounding by half-sibling regression', Proceedings of the National Academy of Sciences, 113(27), 7391-7398.
Thomas, C. G. (2002), 'Noise reduction in BOLD-based fMRI using component analysis', Neuroimage, 17(3), 1521-1537.