Analysis of fMRI Data With Drift: Modified General Linear Model and Bayesian Estimator

The slowly varying drift poses a major problem in the analysis of functional magnetic resonance imaging (fMRI) data. In this paper, based on the observation that noise in fMRI is long memory fractional noise and the slowly varying drift resides in a subspace spanned only by large scale wavelets, we examine a modified general linear model (GLM) in wavelet domain under Bayesian framework. This modified model estimates the activation parameters at each scale of wavelet decomposition. Then, a model selection criterion based on the results from the modified scheme is proposed to model the drift. Results obtained from simulated as well as real fMRI data show that the proposed Bayesian estimator can accurately capture the noise structure, and hence, result in robust estimation of the parameters in GLM. Besides, the proposed model selection criterion works well and could efficiently remove the drift.

[1]  Thomas M. Talavage,et al.  Simulation of human respiration in fMRI with a mechanical model , 2002, IEEE Transactions on Biomedical Engineering.

[2]  S. Mallat.  A wavelet tour of signal processing , 1998 .

[3]  K. Jellinger,et al.  Functional magnetic resonance imaging: an introduction to methods , 2003 .

[4]  J. Duyn,et al.  Investigation of Low Frequency Drift in fMRI Signal , 1999, NeuroImage.

[5]  L. Shah,et al.  Functional magnetic resonance imaging. , 2010, Seminars in roentgenology.

[6]  T A Carpenter,et al.  Colored noise and computational inference in neurophysiological (fMRI) time series analysis: Resampling methods in time and wavelet domains , 2001, Human brain mapping.

[7]  S. Ogawa,et al.  Oxygenation‐sensitive contrast in magnetic resonance image of rodent brain at high magnetic fields , 1990, Magnetic resonance in medicine.

[8]  E. Bullmore,et al.  Wavelets and functional magnetic resonance imaging of the human brain , 2004, NeuroImage.

[9]  A. Walden,et al.  Wavelet Analysis and Synthesis of Stationary Long-Memory Processes , 1996 .

[10]  Clifford M. Hurvich,et al.  Regression and time series model selection in small samples , 1989 .

[11]  Ryali Srikanth,et al.  Wavelet-based Estimation of Hemodynamic Response Function from Fmri Data , 2006, Int. J. Neural Syst..

[12]  François G. Meyer.  Wavelet-based estimation of a semiparametric generalized linear model of fMRI time-series , 2003, IEEE Transactions on Medical Imaging.

[13]  R. Stephenson.  A and V , 1962, The British journal of ophthalmology.

[14]  Mark W. Woolrich,et al.  Multilevel linear modelling for FMRI group analysis using Bayesian inference , 2004, NeuroImage.

[15]  A. Dale,et al.  Deconvolution of Event-Related fMRI Responses in Fast-Rate Experimental Designs: Tracking Amplitude Variations , 2000, Journal of Cognitive Neuroscience.

[16]  George Eastman House,et al.  Sparse Bayesian Learning and the Relevan e Ve tor Ma hine , 2001 .

[17]  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.

[18]  Karl J. Friston,et al.  Classical and Bayesian Inference in Neuroimaging: Theory , 2002, NeuroImage.

[19]  Emery N. Brown,et al.  Nonstationary noise estimation in functional MRI , 2005, NeuroImage.

[20]  E. Bullmore,et al.  Wavelets and statistical analysis of functional magnetic resonance images of the human brain , 2003, Statistical methods in medical research.

[21]  Karl J. Friston,et al.  Classical and Bayesian Inference in Neuroimaging: Applications , 2002, NeuroImage.

[22]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[23]  Patrick Flandrin,et al.  Wavelet analysis and synthesis of fractional Brownian motion , 1992, IEEE Trans. Inf. Theory.

[24]  Gregory W. Wornell,et al.  A Karhunen-Loève-like expansion for 1/f processes via wavelets , 1990, IEEE Trans. Inf. Theory.

[25]  A.H. Tewfik,et al.  Correlation structure of the discrete wavelet coefficients of fractional Brownian motion , 1992, IEEE Trans. Inf. Theory.

[26]  Yul-Wan Sung,et al.  Functional magnetic resonance imaging , 2004, Scholarpedia.

[27]  Paul M. Matthews,et al.  Functional magnetic resonance imaging: An introduction to methods , 2001 .