Bayesian variational approximation for the joint detection estimation of brain activity in fMRI

We address the issue of jointly detect brain activity and estimate brain hemodynamics from functional MRI data. To this end, we adopt the so-called JDE framework introduced in [1] and augmented in [2] with hidden Markov field models to account for spatial dependencies between voxels. This latter spatial addition is essential but also responsible for high computation costs. To face the intractability induced by Markov models, inference in [2] is based on intensive simulation methods (MCMC). In this work we propose an alternative to face this limitation by recasting the JDE framework into a missing data framework and to derive an EM algorithm for inference. We address the intractability issue by considering variational approximations. We show that the derived Variational EM algorithm outperforms the MCMC procedure on realistic artificial fMRI data.