title: Nonlinear Bayesian estimation of BOLD signal under non-Gaussian noise.
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.
authors.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.
authors.forename: Ali Fahim
authors.initials: AF
authors.lastname: Khan
authors.affiliation: School of Electrical Engineering and Computer Science, National University of Sciences and Technology, Islamabad 44000, Pakistan.
authors.forename: Muhammad Shahzad
authors.initials: MS
authors.lastname: Younis
authors.affiliation: Department of Telecommunication Engineering, University of Engineering and Technology, Taxila 47080, Pakistan.
authors.forename: Khalid Bashir
authors.initials: KB
authors.lastname: Bajwa
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D001921:Brain / Q000098:blood supply* / Q000502:physiology; D006439:Hemodynamics; D006801:Humans; D008279:Magnetic Resonance Imaging; D008954:Models, Biological; D015233:Models, Statistical; D016011:Normal Distribution; D010100:Oxygen / Q000097:blood*; D010101:Oxygen Consumption
chemical_list: D010100:Oxygen