We introduce a novel non-iterative algorithm for the fast and accurate reconstruction of non-uniformly sampled MRI data. The proposed scheme derives the reconstructed image as the non-uniform inverse Fourier transform of a compensated dataset. We derive each sample in the compensated dataset as a weighted linear combination of a few measured kspace samples. The specific k-space samples and the weights involved in the linear combination are derived such that the reconstruction error is

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... The computational complexity of the proposed scheme is comparable to that of gridding. At the same time, it provides significantly improved accuracy and is considerably more robust to noise and undersampling. The advantages of the proposed scheme makes it ideally suited for the fast reconstruction of large multidimensional datasets, which routinely arise in applications such as f-MRI and MR spectroscopy. The comparisons with state of the art algorithms on numerical phantoms and MRI data clearly demonstrate the performance improvement.