Compressed sensing combined with parallel imaging has allowed significant reduction in MRI scan time. However, image reconstruction remains challenging and common methods rely on a coil calibration step. In this work, we focus on calibrationless reconstruction methods that promote group sparsity. The latter have allowed theoretical improvements in CS recovery guarantees. Here, we compare the performances of several regularization terms (group-LASSO, sparse group-LASSO and OSCAR) that define with the data consistency term the convex but nonsmooth objective function to be minimized. The same primal-dual algorithm can be used to perform this minimization. Our results demonstrate that OSCAR-based reconstruction is competitive with state-of-the-art $$$\ell_1$$$-ESPIRiT.