Detrend-Free Hemodynamic Data Assimilation of Two-Stage Kalman Estimator

  • Hu Zhenghui
  • Shi Pengcheng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6892)


Spurious temporal drift is abundant in fMRI data, and its removal is a critical preprocessing step in fMRI data assimilation due to the sparse nature and the complexity of the data. Conventional data-driven approaches rest upon specific assumptions of the drift structure and signal statistics, and may lead to inaccurate results. In this paper we present an approach to the assimilation of nonlinear hemodynamic system, with special attention on drift. By treating the drift variation as a random-walk process, the assimilation problem was translated into the identification of a nonlinear system in the presence of time varying bias. We developed two-stage unscented Kalman filter (UKF) to efficiently handle this problem. In this framework the assimilation can implement with original fMRI data without detrending preprocessing. The fMRI responses and drift were estimated simultaneously in an assimilation cycle. The efficacy of this approach is demonstrated in synthetic and real fMRI experiments. Results show that the joint estimation strategy produces more accurate estimation of physiological states, fMRI response and drift than separate processing due to no assumption of structure of the drift that is not available in fMRI data.


fMRI Data Unscented Kalman Filter fMRI Signal Linear Drift fMRI Response 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Bazargani, N., Nasratinia, A., Gopinath, K., Briggs, R.W.: FMRI Baseline Drift Estimation Method by MDL Principle. In: 4th IEEE International Symposium on Biomedical Imaging (ISBI), Washington, D.C., USA, pp. 472–475 (2007)Google Scholar
  2. 2.
    Buxton, R.B., Wong, E.C., Frank, L.R.: Dynamics of Blood Flow and Oxygenation Changes During Brain Activation: The Balloon Model.. Magnetic Resonance in Medicine 39, 855–864 (1998)CrossRefGoogle Scholar
  3. 3.
    Friedland, B.: Treatment of Bias in Recursive Filtering. IEEE Transactions on Automatic Control 14(4), 359–367 (1969)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Friston, K.J., Mechelli, A., Turner, R., Price, C.J.: Nonlinear Responses in fMRI: The Balloon Model, Volterra Kernels, and Other Hemodynamics.. NeuroImage 12, 466–477 (2000)CrossRefGoogle Scholar
  5. 5.
    Hsieh, C.S.: General Two-stage Extended Kalman Filters. IEEE Transactions on Automatic Control 48(2), 289–293 (2003)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Hu, Z.H., Shi, P.C.: Nonlinear Analysis of BOLD Signal: Biophysical Modeling, Physiological States, and Functional Activation. In: Ayache, N., Ourselin, S., Maeder, A. (eds.) MICCAI 2007, Part II. LNCS, vol. 4792, pp. 734–741. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  7. 7.
    Hu, Z.H., Shi, P.C.: Sensitivity Analysis for Biomedical Models. IEEE Transactions on Medical Imaging 29(11), 1870–1881 (2010)CrossRefGoogle Scholar
  8. 8.
    Julier, S.J., Uhlmann, J.K.: Unscented Filtering and Nonlinear Estimation. Proceeding of the IEEE 92(3), 401–422 (2004)CrossRefGoogle Scholar
  9. 9.
    Moradkhani, H., Sorooshian, S., Gupta, H.V., Houser, P.R.: Dual State-parameter Estimation of Hydrological Models Using Ensemble Kalman Filter. Advance in Water Resouces 28, 135–147 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Hu Zhenghui
    • 1
  • Shi Pengcheng
    • 2
  1. 1.State Key Laboratory of Modern Optical InstrumentationZhejiang UniversityHangzhouChina
  2. 2.Rochester Institute of TechnologyB. Thomas Golisano College of Computing and Information SciencesRochesterUSA

Personalised recommendations