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Nonlinear Bayesian estimation of BOLD signal under non-Gaussian noise.

Khan AF, Younis MS, Bajwa KB - Comput Math Methods Med (2015)

Bottom Line: Though more feasible, the assumption may cause the designed filter to perform poorly if made to work under non-Gaussian environment.The proposed filter MAGSF and the celebrated EKF are put to test by performing joint optimal Bayesian filtering to estimate both the states and parameters governing the hemodynamic model under non-Gaussian environment.Analyses using both the synthetic and real data reveal superior performance of the MAGSF as compared to EKF.

View Article: PubMed Central - PubMed

Affiliation: School of Electrical Engineering and Computer Science, National University of Sciences and Technology, Islamabad 44000, Pakistan ; Department of Electrical Engineering, Institute of Space Technology, Islamabad 44000, Pakistan.

ABSTRACT
Modeling the blood oxygenation level dependent (BOLD) signal has been a subject of study for over a decade in the neuroimaging community. Inspired from fluid dynamics, the hemodynamic model provides a plausible yet convincing interpretation of the BOLD signal by amalgamating effects of dynamic physiological changes in blood oxygenation, cerebral blood flow and volume. The nonautonomous, nonlinear set of differential equations of the hemodynamic model constitutes the process model while the weighted nonlinear sum of the physiological variables forms the measurement model. Plagued by various noise sources, the time series fMRI measurement data is mostly assumed to be affected by additive Gaussian noise. Though more feasible, the assumption may cause the designed filter to perform poorly if made to work under non-Gaussian environment. In this paper, we present a data assimilation scheme that assumes additive non-Gaussian noise, namely, the e-mixture noise, affecting the measurements. The proposed filter MAGSF and the celebrated EKF are put to test by performing joint optimal Bayesian filtering to estimate both the states and parameters governing the hemodynamic model under non-Gaussian environment. Analyses using both the synthetic and real data reveal superior performance of the MAGSF as compared to EKF.

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Framework of the MAGSF.
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fig2: Framework of the MAGSF.

Mentions: Figure 2 shows the framework of the proposed filter. Unlike the AGSF that has a bank of Kalman filters, the MAGSF has a bank of extended Kalman filters each tuned to a specific term of the Gaussian mixture. The filter is specifically designed to combat Gaussian process noise but non-Gaussian measurement noise. First the filter is initialized with the initial conditions and P(0∣0) = P(0) where P is the error covariance.


Nonlinear Bayesian estimation of BOLD signal under non-Gaussian noise.

Khan AF, Younis MS, Bajwa KB - Comput Math Methods Med (2015)

Framework of the MAGSF.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4321086&req=5

fig2: Framework of the MAGSF.
Mentions: Figure 2 shows the framework of the proposed filter. Unlike the AGSF that has a bank of Kalman filters, the MAGSF has a bank of extended Kalman filters each tuned to a specific term of the Gaussian mixture. The filter is specifically designed to combat Gaussian process noise but non-Gaussian measurement noise. First the filter is initialized with the initial conditions and P(0∣0) = P(0) where P is the error covariance.

Bottom Line: Though more feasible, the assumption may cause the designed filter to perform poorly if made to work under non-Gaussian environment.The proposed filter MAGSF and the celebrated EKF are put to test by performing joint optimal Bayesian filtering to estimate both the states and parameters governing the hemodynamic model under non-Gaussian environment.Analyses using both the synthetic and real data reveal superior performance of the MAGSF as compared to EKF.

View Article: PubMed Central - PubMed

Affiliation: School of Electrical Engineering and Computer Science, National University of Sciences and Technology, Islamabad 44000, Pakistan ; Department of Electrical Engineering, Institute of Space Technology, Islamabad 44000, Pakistan.

ABSTRACT
Modeling the blood oxygenation level dependent (BOLD) signal has been a subject of study for over a decade in the neuroimaging community. Inspired from fluid dynamics, the hemodynamic model provides a plausible yet convincing interpretation of the BOLD signal by amalgamating effects of dynamic physiological changes in blood oxygenation, cerebral blood flow and volume. The nonautonomous, nonlinear set of differential equations of the hemodynamic model constitutes the process model while the weighted nonlinear sum of the physiological variables forms the measurement model. Plagued by various noise sources, the time series fMRI measurement data is mostly assumed to be affected by additive Gaussian noise. Though more feasible, the assumption may cause the designed filter to perform poorly if made to work under non-Gaussian environment. In this paper, we present a data assimilation scheme that assumes additive non-Gaussian noise, namely, the e-mixture noise, affecting the measurements. The proposed filter MAGSF and the celebrated EKF are put to test by performing joint optimal Bayesian filtering to estimate both the states and parameters governing the hemodynamic model under non-Gaussian environment. Analyses using both the synthetic and real data reveal superior performance of the MAGSF as compared to EKF.

Show MeSH