Robust Estimation of HDR in fMRI using $H^\infty$ Filters

Estimation and detection of the hemodynamic response (HDR) are of great importance in functional MRI (fMRI) data analysis. In this paper, we propose the use of three H ∞ adaptive filters (finite memory, exponentially weighted, and time-varying) for accurate estimation and detection of the HDR. The H ∞ approach is used because it safeguards against the worst case disturbances and makes no assumptions on the (statistical) nature of the signals [B. Hassibi and T. Kailath, in Proc. ICASSP, 1995, vol. 2, pp. 949-952; T. Ratnarajah and S. Puthusserypady, in Proc. 8th IEEE Workshop DSP, 1998, pp. 1483-1487]. Performances of the proposed techniques are compared to the conventional t-test method as well as the well-known LMSs and recursive least squares algorithms. Extensive numerical simulations show that the proposed methods result in better HDR estimations and activation detections.

[1]  D. Heeger,et al.  Linear Systems Analysis of Functional Magnetic Resonance Imaging in Human V1 , 1996, The Journal of Neuroscience.

[2]  J. Mazziotta,et al.  Brain Mapping: The Methods , 2002 .

[3]  Ali H. Sayed,et al.  H∞ optimality of the LMS algorithm , 1996, IEEE Trans. Signal Process..

[4]  A. Dale,et al.  Selective averaging of rapidly presented individual trials using fMRI , 1997, Human brain mapping.

[5]  Jean-Baptiste Poline,et al.  Unsupervised robust nonparametric estimation of the hemodynamic response function for any fMRI experiment , 2003, IEEE Transactions on Medical Imaging.

[6]  Karl J. Friston,et al.  Nonlinear Responses in fMRI: The Balloon Model, Volterra Kernels, and Other Hemodynamics , 2000, NeuroImage.

[7]  Karl J. Friston,et al.  Analysis of fMRI Time-Series Revisited—Again , 1995, NeuroImage.

[8]  Bruce R. Rosen,et al.  Comparison of two convolution models for fMRI time series , 1997 .

[9]  R. Buxton.  Introduction to Functional Magnetic Resonance Imaging: Principles and Techniques , 2002 .

[10]  Lars Kai Hansen,et al.  Modelling the Haemodynamic Response in fMRI with Smooth FIR Filters , 2000, IEEE Trans. Medical Imaging.

[11]  Stephen M. Smith,et al.  Functional MRI : an introduction to methods , 2002 .

[12]  R. Turner,et al.  Event-Related fMRI: Characterizing Differential Responses , 1998, NeuroImage.

[13]  P. Bandettini,et al.  Spatial Heterogeneity of the Nonlinear Dynamics in the FMRI BOLD Response , 2001, NeuroImage.

[14]  J C Gore,et al.  An roc approach for evaluating functional brain mr imaging and postprocessing protocols , 1995, Magnetic resonance in medicine.

[15]  Babak Hassibi,et al.  Adaptive Filtering with an Hm Criterion , 1995 .

[16]  Sadasivan Puthusserypady,et al.  Adaptive spatiotemporal modelling and estimation of the event-related fMRI responses , 2007, Signal Process..

[17]  J B Poline,et al.  Transient Activity in the Human Calcarine Cortex During Visual-Mental Imagery: An Event-Related fMRI Study , 2000, Journal of Cognitive Neuroscience.

[18]  E. Bullmore,et al.  Identifying Rate-Limiting Nodes in Large-Scale Cortical Networks for Visuospatial Processing: An Illustration using fMRI , 2001, Journal of Cognitive Neuroscience.

[19]  Karl J. Friston,et al.  Analysis of fMRI Time-Series Revisited , 1995, NeuroImage.

[20]  T. Sejnowski,et al.  Single-Trial Variability in Event-Related BOLD Signals , 2002, NeuroImage.

[21]  Tianzi Jiang,et al.  Single-trial variable model for event-related fMRI data analysis , 2005, IEEE Transactions on Medical Imaging.

[22]  Lars Kai Hansen,et al.  Modeling the hemodynamic response in fMRI using smooth FIR filters , 2000, IEEE Transactions on Medical Imaging.

[23]  Mark D'Esposito,et al.  Variation of BOLD hemodynamic responses across subjects and brain regions and their effects on statistical analyses , 2004, NeuroImage.

[24]  Kayvan Najarian,et al.  Biomedical Signal and Image Processing , 2005 .

[25]  Thomas Kailath,et al.  Adaptive filtering with a H/sup /spl infin// criterion , 1994, Proceedings of 1994 28th Asilomar Conference on Signals, Systems and Computers.

[26]  J. Haxby,et al.  fMRI study of face perception and memory using random stimulus sequences. , 1998, Journal of neurophysiology.

[27]  R. Buxton,et al.  Modeling the hemodynamic response to brain activation , 2004, NeuroImage.

[28]  Todd B. Parrish,et al.  Hemodynamic response function in patients with stroke-induced aphasia: Implications for fMRI data analysis , 2007, NeuroImage.

[29]  G. Wnek,et al.  Encyclopedia of biomaterials and biomedical engineering , 2008 .