Parallel MRI noise correction: an extension of the LMMSE to non central chi distributions

Parallel MRI leads to magnitude data corrupted by noise described in most cases as following a Rician or a non central chi distribution. And yet, very few correction methods perform a non central chi noise removal. However, this correction step, adapted to the correct noise model, is of very much importance, especially when working with Diffusion Weighted MR data yielding a low SNR. We propose an extended Linear Minimum Mean Square Error estimator (LMMSE), which is adapted to deal with non central chi distributions. We demonstrate on simulated and real data that the extended LMMSE outperforms the original LMMSE on images corrupted by a non central chi noise.