Background: Parallel magnetic resonance imaging (MRI) is a fast imaging technique that helps acquiring highly resolved images in space/time. Its performance depends on the reconstruction algorithm, which can proceed either inthe k-space or in the image domain.Objective: and methods To improve the performance of the widely used SENSE algorithm, 2D regularization in thewavelet domain has been investigated. In this paper, we first extend this approach to 3D-wavelet representationsand the 3D sparsity-promoting regularization term, in order to address reconstruction artifacts that propagate acrossadjacent slices. The resulting optimality criterion is convex but nonsmooth, and we resort to the parallel proximalalgorithm to minimize it. Second, to account for temporal correlation between successive scans in functional MRI(fMRI), we extend our first contribution to 3D +t acquisition schemes by incorporating a prior along the time axis into the objective function.Results: Our first method (3D-UWR-SENSE) is validated on T1-MRI anatomical data for gray/white matter segmentation.The second method (4D-UWR-SENSE) is validated for detecting evoked activity during a fast eventrelatedfunctional MRI protocol.Conclusion: We show that our algorithm outperforms the SENSE reconstruction at the subject and group levels (15 subjects) for different contrasts of interest (motor or computation tasks) and two parallel acceleration factors (R = 2 and R = 4) on 2x2x3 mm3 echo planar imaging (EPI) images.