Abstract : To reduce scanning time and/or improve spatial/temporal resolution in some Magnetic Resonance Imaging (MRI) applications, parallel MRI acquisition techniques with multiple coils acquisition have emerged since the early 1990s as powerful imaging methods that allow a faster acquisition process. In these techniques, the full FOV image has to be reconstructed from the resulting acquired undersampled k-space data. To this end, several reconstruction techniques have been proposed such as the widely-used SENSitivity Encoding (SENSE) method. However, the reconstructed image generally presents artifacts when perturbations occur in both the measured data and the estimated coil sensitivity profiles. In this paper, we aim at achieving accurate image reconstruction under degraded experimental conditions (low magnetic field and high reduction factor), in which neither the SENSE method nor the Tikhonov regularization in the image domain give convincing results. To this end, we present a novel method for SENSE-based reconstruction which proceeds with regularization in the complex wavelet domain by promoting sparsity. The proposed approach relies on a fast algorithm that enables the minimization of regularized non-differentiable criteria including more general penalties than a classical l(1) term. To further enhance the reconstructed image quality, local convex constraints are added to the regularization process. In vivo human brain experiments carried out on Gradient-Echo (GRE) anatomical and Echo Planar Imaging (EPI) functional MRI data at 1.5 T indicate that our algorithm provides reconstructed images with reduced artifacts for high reduction factors. (C) 2010 Elsevier B.V. All rights reserved.