High resolution robust and smooth precision matrices to capture functional connectivity

Nicolas Honnorat, Christos Davatzikos

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Resting-state functional MRI (fMRI) provides a crucial insight into brain organization, by offering a mean to measure the functional connectivity between brain regions. A popular measure, the effective functional connectivity, is derived from the precision matrix obtained by inverting the correlations between brain regions fMRI signals. This approach has been widely adopted to build brain connectomes for large populations. For small populations and single fMRI scans, however, the significant amount of noise in the fMRI scans reduces the quality of the precision matrices, and the non-invertibility of the correlation matrices calls for more sophisticated precision estimators. These issues are especially dramatic at full brain resolution. In this work, we investigate several approaches to improve full resolution precision matrices derived from single fMRI scans. First, we compare three approaches for the computation of the correlation matrix. Then, we investigate two regularized inversions, in combination with a correlation shrinkage and two spatial smoothing strategies. During these experiments, the quality of precision matrices obtained for random fMRI half scans was measured by their generalization: their fit to the unseen time points. Our experiments, using ten high resolutions scans of the Human Connectome Project, indicate that correlation shrinkage strongly improves precision generalization. The two regularizations are associated with similar generalization. Smoothing the fMRI signal before the inversion deteriorates the generalization whereas a penalty directly improving the smoothness of the precision matrix can improve the generalization, in particular for short time series and in combination with shrinkage.

Original languageEnglish (US)
Title of host publicationMedical Imaging 2018
Subtitle of host publicationImage Processing
EditorsElsa D. Angelini, Elsa D. Angelini, Bennett A. Landman
ISBN (Electronic)9781510616370
StatePublished - 2018
Externally publishedYes
EventMedical Imaging 2018: Image Processing - Houston, United States
Duration: Feb 11 2018Feb 13 2018

Publication series

NameProgress in Biomedical Optics and Imaging - Proceedings of SPIE
ISSN (Print)1605-7422


ConferenceMedical Imaging 2018: Image Processing
Country/TerritoryUnited States


  • covariance shrinkage
  • effective connectivity
  • functional MRI

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics
  • Biomaterials
  • Radiology Nuclear Medicine and imaging


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