The method of enforcing sparsity during magnetic resonance imaging reconstruction has been successfully applied to partially parallel imaging (PPI) techniques to reduce noise and artifact levels and hence to achieve even higher acceleration factors. However, there are two major problems in the existing sparsity-constrained PPI techniques: speed and robustness. By introducing an auxiliary variable and decomposing the original minimization problem into two subproblems that are much easier to solve, a fast and robust numerical algorithm for sparsity-constrained PPI technique is developed in this work. The specific implementation for a conventional Cartesian trajectory data set is named self-feeding Sparse Sensitivity Encoding (SENSE). The computational cost for the proposed method is two conventional SENSE reconstructions plus one spatially adaptive image denoising procedure. With reconstruction time approximately doubled, images with a much lower root mean square error (RMSE) can be achieved at high acceleration factors. Using a standard eight-channel head coil, a net acceleration factor of 5 along one dimension can be achieved with low RMSE. Furthermore, the algorithm is insensitive to the choice of parameters. This work improves the clinical applicability of SENSE at high acceleration factors. Magn Reson Med 64:1078-1088, 2010. V C 2010 WileyLiss, Inc.Key words: partially parallel imaging; g-factor; sparsity constraint; prior information; compressed sensing; numerical algorithm Partially parallel imaging (PPI) techniques (1,2) are being routinely used to achieve increased image resolution, decreased motion artifacts, and shorter scan time in magnetic resonance imaging (MRI). However, PPI techniques reduce acquisition time at the cost of a reduction in signal-to-noise ratio (SNR). With an increase in the acceleration factor, the increase in noise and artifact levels can become significant, thereby reducing the diagnostic quality of the image. To avoid significant artifacts and noise amplification, the acceleration factor, R, is typically restricted to values far below the theoretical limit (i.e., the number of coil elements). For example, acceleration factors are no more than 3 in most clinical exams for the widely available eight-channel head coil. To reduce the noise and artifact levels, techniques of enforcing sparsity in PPI reconstruction have recently been proposed (3-6), where ''sparsity'' means that the to-be-reconstructed image has a sparse representation in a known and fixed mathematical transform domain (7). These techniques enforce the sparsities of the to-be-reconstructed image in finite difference domain and wavelet transform domain by minimizing its total variation (TV) norm and the L 1 norm of its wavelet transform. The sparsity constraints play an important role in lowering the noise/artifact levels of the reconstructed images. Meanwhile, a data fidelity term is used to preserve image contrast and resolution. Sparsity constraints and data fidelity are balanced by the parameters that are the weigh...