Non-stationary Gaussian spatio-temporal modeling of fMRI data

In functional magnetic resonance imaging (fMRI), modeling of the complex link between neuronal activity and its hemodynamic expression via the neurovascular coupling usually requires the use of elaborated models. To avoid linear assumptions and a priori modeling of this expected hemodynamic signal, Bayesian approaches have recently improved their accuracy in estimating and detecting brain activation. Recent studies, using Markov random field (MRF) to represent activated brain voxels and likelihoods to find the maximum a posteriori (MAP) estimation of model parameters, provided superior efficiency in comparison with the context-free and the statistical parametric mapping (SPM) approaches. We propose another approach for detecting brain activity by introducing non-Gaussian and non-stationary Gaussian image models that exploit local subband image statistics in the non-decimated wavelet domain. These statistical models, being very simple and tractable, have demonstrated state-of-the-art performance in a number of applications including lossy image compression, denoising and digital watermarking. Such an approach yields close form analytical solutions with low computational complexity that makes it very attractive in neuropsychological research allowing to obtain theoretical performance limits. These models in the scope of the Bayesian estimation framework are applied on synthetic fMRI data corrupted by an additive white Gaussian noise (AWGN) with varying variance and on real fMRI data obtained from a motor preparation task. Comparison of the results with those obtained using SPM maps demonstrates the high efficiency of the proposed method.