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To develop and optimize a new modification of GRAPPA (generalized autocalibrating partially parallel acquisitions) MR reconstruction algorithm named “Robust GRAPPA.”In Robust GRAPPA, k-space data points were weighted before the reconstruction. Small or zero weights were assigned to “outliers” in k-space. We implemented a Slow Robust GRAPPA method, which iteratively reweighted the k-space data. It was compared to an ad hoc Fast Robust GRAPPA method, which eliminated (assigned zero weights to) a fixed percentage of k-space “outliers” following an initial estimation procedure. In comprehensive experiments the new algorithms were evaluated using the perceptual difference model (PDM), whereby image quality was quantitatively compared to the reference image. Independent variables included algorithm type, total reduction factor, outlier ratio, center filling options, and noise across multiple image datasets, providing 10,800 test images for evaluation.The Fast Robust GRAPPA method gave results very similar to Slow Robust GRAPPA, and showed significant improvements as compared to regular GRAPPA. Fast Robust GRAPPA added little computation time compared with regular GRAPPA.Robust GRAPPA was proposed and proved useful for improving the reconstructed image quality. PDM was helpful in designing and optimizing the MR reconstruction algorithms. J. Magn. Reson. Imaging 2008;27:1412–1420. © 2008 Wiley-Liss, Inc.