Variational solution to the joint detection estimation of brain activity in fMRI

We address the issue of jointly detecting brain activity and estimating underlying brain hemodynamics from functional MRI data. We adopt the so-called Joint Detection Estimation (JDE) framework that takes spatial dependencies between voxels into account. We recast the JDE into a missing data framework and derive a Variational Expectation-Maximization (VEM) algorithm for its inference. It follows a new algorithm that has interesting advantages over the previously used intensive simulation methods (Markov Chain Monte Carlo, MCMC): tests on artificial data show that the VEM-JDE is more robust to model mis-specification while additional tests on real data confirm that it achieves similar performance in much less computation time.