  In standard clinical within-subject analyses of event-related fMRI data, two
steps are usually performed separately: detection of brain activity and
estimation of the hemodynamic response. Because these two steps are inherently
linked, we adopt the so-called region-based Joint Detection-Estimation (JDE)
framework that addresses this joint issue using a multivariate inference for
detection and estimation. JDE is built by making use of a regional bilinear
generative model of the BOLD response and constraining the parameter estimation
by physiological priors using temporal and spatial information in a Markovian
modeling. In contrast to previous works that use Markov Chain Monte Carlo
(MCMC) techniques to approximate the resulting intractable posterior
distribution, we recast the JDE into a missing data framework and derive a
Variational Expectation-Maximization (VEM) algorithm for its inference. A
variational approximation is used to approximate the Markovian model in the
unsupervised spatially adaptive JDE inference, which allows fine automatic
tuning of spatial regularisation parameters. It follows a new algorithm that
exhibits interesting properties compared to the previously used MCMC-based
approach. Experiments on artificial and real data show that VEM-JDE is robust
to model mis-specification and provides computational gain while maintaining
good performance in terms of activation detection and hemodynamic shape
recovery.
