Robust Extrapolation Scheme for Fast Estimation of 3D Ising Field Partition Functions: Application to Within-Subject fMRI Data Analysis

  • Laurent Risser
  • Thomas Vincent
  • Philippe Ciuciu
  • Jérôme Idier
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5761)

Abstract

In this paper, we present a fast numerical scheme to estimate Partition Functions (PF) of 3D Ising fields. Our strategy is applied to the context of the joint detection-estimation of brain activity from functional Magnetic Resonance Imaging (fMRI) data, where the goal is to automatically recover activated regions and estimate region-dependent hemodynamic filters. For any region, a specific binary Markov random field may embody spatial correlation over the hidden states of the voxels by modeling whether they are activated or not. To make this spatial regularization fully adaptive, our approach is first based upon a classical path-sampling method to approximate a small subset of reference PFs corresponding to prespecified regions. Then, the proposed extrapolation method allows us to approximate the PFs associated with the Ising fields defined over the remaining brain regions. In comparison with preexisting approaches, our method is robust to topological inhomogeneities in the definition of the reference regions. As a result, it strongly alleviates the computational burden and makes spatially adaptive regularization of whole brain fMRI datasets feasible.

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References

  1. 1.
    Vincent, T., Ciuciu, P., Idier, J.: Spatial mixture modelling for the joint detection-estimation of brain activity in fMRI. In: 32th Proc. IEEE ICASSP, Honolulu, Hawaii, vol. I, pp. 325–328 (2007)Google Scholar
  2. 2.
    Meng, X., Wong, W.: Simulating ratios of normalizing constants via a simple identity: a theoretical exploration. Statistica Sinica 6, 831–860 (1996)MathSciNetMATHGoogle Scholar
  3. 3.
    Gelman, A., Meng, X.L.: Simulating normalizing constants: from importance sampling to bridge sampling to path sampling. Statistical Science 13, 163–185 (1998)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Fernández, S., Green, P.J.: Modelling spatially correlated data via mixtures: a Bayesian approach. J. R. Statist. Soc. B 64, 805–826 (2002)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Woolrich, M., Behrens, T., Beckmann, C., Smith, S.: Mixture models with adaptive spatial regularization for segmentation with an application to fMRI data. IEEE Trans. Med. Imag. 24, 1–11 (2005)CrossRefGoogle Scholar
  6. 6.
    Makni, S., Idier, J., Vincent, T., Thirion, B., Dehaene-Lambertz, G., Ciuciu, P.: A fully Bayesian approach to the parcel-based detection-estimation of brain activity in fMRI. Neuroimage 41, 941–969 (2008)CrossRefGoogle Scholar
  7. 7.
    Thirion, B., Flandin, G., Pinel, P., Roche, A., Ciuciu, P., Poline, J.B.: Dealing with the shortcomings of spatial normalization: Multi-subject parcellation of fMRI datasets. Hum. Brain Mapp. 27, 678–693 (2006)CrossRefGoogle Scholar
  8. 8.
    Trillon, A., Idier, J., Peureux, P.: Unsupervised Bayesian 3D reconstruction for non-destructive evaluation using gammagraphy. In: EUSIPCO, Suisse (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Laurent Risser
    • 1
    • 2
    • 3
  • Thomas Vincent
    • 1
    • 2
  • Philippe Ciuciu
    • 1
    • 2
  • Jérôme Idier
    • 3
  1. 1.NeuroSpin/CEAGif-sur-YvetteFrance
  2. 2.IFR 49, Institut d’Imagerie NeurofonctionnelleParisFrance
  3. 3.IRCCyN/CNRSNantesFrance

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