  Parallel MRI is a fast imaging technique that enables the acquisition of
highly resolved images in space. It relies on $k$-space undersampling and
multiple receiver coils with complementary sensitivity profiles in order to
reconstruct a full Field-Of-View (FOV) image. The performance of parallel
imaging mainly depends on the reconstruction algorithm, which can proceed
either in the original $k$-space (GRAPPA, SMASH) or in the image domain
(SENSE-like methods). To improve the performance of the widely used SENSE
algorithm, 2D- or slice-specific regularization in the wavelet domain has been
efficiently investigated. In this paper, we extend this approach using
3D-wavelet representations in order to handle all slices together and address
reconstruction artifacts which propagate across adjacent slices. The extension
also accounts for temporal correlations that exist between successive scans in
functional MRI (fMRI). The proposed 4D reconstruction scheme is fully
\emph{unsupervised} in the sense that all regularization parameters are
estimated in the maximum likelihood sense on a reference scan. The gain induced
by such extensions is first illustrated on EPI image reconstruction but also
measured in terms of statistical sensitivity during a fast event-related fMRI
protocol. The proposed 4D-UWR-SENSE algorithm outperforms the SENSE
reconstruction at the subject and group-levels (15 subjects) for different
contrasts of interest and using different parallel acceleration factors on
$2\times2\times3$mm$^3$ EPI images.
