A Sparse and Spatially Constrained Generative Regression Model for fMRI Data Analysis

In this study, we present an advanced Bayesian framework for the analysis of functional magnetic resonance imaging (fMRI) data that simultaneously employs both spatial and sparse properties. The basic building block of our method is the general linear regression model that constitutes a well-known probabilistic approach. By treating regression coefficients as random variables, we can apply an enhanced Gibbs distribution function that captures spatial constrains and at the same time allows sparse representation of fMRI time series. The proposed scheme is described as a maximum a posteriori approach, where the known expectation maximization algorithm is applied offering closed-form update equations for the model parameters. We have demonstrated that our method produces improved performance and functional activation detection capabilities in both simulated data and real applications.

[1]  Karl J. Friston,et al.  Statistical parametric mapping , 2013 .

[2]  J. Lewin.  Functional MRI: An introduction to methods , 2003 .

[3]  L. Astrakas,et al.  T2 relaxometry and fMRI of the brain in late-onset restless legs syndrome , 2008, Neurology.

[4]  Polina Golland,et al.  Combining spatial priors and anatomical information for fMRI detection , 2010, Medical Image Anal..

[5]  Jianfeng Feng,et al.  Voxel Selection in fMRI Data Analysis Based on Sparse Representation , 2009, IEEE Transactions on Biomedical Engineering.

[6]  Otto Opitz,et al.  Exploratory Data Analysis in Empirical Research , 2002 .

[7]  Mark W. Woolrich,et al.  Fully Bayesian spatio-temporal modeling of FMRI data , 2004, IEEE Transactions on Medical Imaging.

[8]  Donald Geman,et al.  Nonlinear image recovery with half-quadratic regularization , 1995, IEEE Trans. Image Process..

[9]  Sadasivan Puthusserypady,et al.  A sparse Bayesian method for determination of flexible design matrix for fMRI data analysis , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[10]  A. Ravishankar Rao,et al.  Prediction and interpretation of distributed neural activity with sparse models , 2009, NeuroImage.

[11]  Sadasivan Puthusserypady,et al.  Analysis of fMRI Data With Drift: Modified General Linear Model and Bayesian Estimator , 2008, IEEE Transactions on Biomedical Engineering.

[12]  Hans Knutsson,et al.  Adaptive analysis of fMRI data , 2003, NeuroImage.

[13]  Tom Heskes,et al.  Efficient Bayesian multivariate fMRI analysis using a sparsifying spatio-temporal prior , 2010, NeuroImage.

[14]  Stephen M. Smith,et al.  Segmentation of brain MR images through a hidden Markov random field model and the expectation-maximization algorithm , 2001, IEEE Transactions on Medical Imaging.

[15]  Karl J. Friston,et al.  Diffusion-based spatial priors for functional magnetic resonance images , 2008, NeuroImage.

[16]  Radford M. Neal.  Pattern Recognition and Machine Learning , 2007, Technometrics.

[17]  N V Hartvig,et al.  Spatial mixture modeling of fMRI data , 2000, Human brain mapping.

[18]  George Eastman House,et al.  Sparse Bayesian Learning and the Relevance Vector Machine , 2001 .

[19]  Florian Steinke,et al.  Bayesian Inference and Optimal Design in the Sparse Linear Model , 2007, AISTATS.

[20]  M. Hallett.  Human Brain Function , 1998, Trends in Neurosciences.

[21]  Gerard J. den Heeten,et al.  Functional magnetic resonance imaging for neurosurgical planning in neurooncology , 2004, European Radiology.

[22]  Karl J. Friston,et al.  Bayesian fMRI time series analysis with spatial priors , 2005, NeuroImage.

[23]  William D. Penny,et al.  Bayesian fMRI data analysis with sparse spatial basis function priors , 2007, NeuroImage.

[24]  Tülay Adali,et al.  Estimating the number of independent components for functional magnetic resonance imaging data , 2007, Human brain mapping.

[25]  Wanmei Ou,et al.  fMRI Detection via Variational EM Approach , 2005 .

[26]  Karl J. Friston,et al.  Variational Bayesian inference for fMRI time series , 2003, NeuroImage.

[27]  Shan Bao-ci.  Independent Component Analysis of Functional MRI Data: An Overview , 2005 .

[28]  T. Shallice,et al.  Face repetition effects in implicit and explicit memory tests as measured by fMRI. , 2002, Cerebral cortex.

[29]  L. Fahrmeir,et al.  Spatial Bayesian Variable Selection With Application to Functional Magnetic Resonance Imaging , 2007 .

[30]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[31]  Jeremy MG Taylor,et al.  Robust Statistical Modeling Using the t Distribution , 1989 .

[32]  Xu Chen,et al.  Bayesian Kernel Methods for Analysis of Functional Neuroimages , 2007, IEEE Transactions on Medical Imaging.

[33]  Xavier Descombes,et al.  fMRI Signal Restoration Using a Spatio-Temporal Markov Random Field Preserving Transitions , 1998, NeuroImage.

[34]  C Gössl,et al.  Bayesian Spatiotemporal Inference in Functional Magnetic Resonance Imaging , 2001, Biometrics.

[35]  Polina Golland,et al.  From Spatial Regularization to Anatomical Priors in fMRI Analysis , 2005, IPMI.

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

[37]  Karl J. Friston,et al.  Posterior probability maps and SPMs , 2003, NeuroImage.

[38]  Sadasivan Puthusserypady,et al.  fMRI Data Analysis With Nonstationary Noise Models: A Bayesian Approach , 2007, IEEE Transactions on Biomedical Engineering.