Parallel MRI noise correction: An extension of the LMMSE to non central χ distributions

Abstract

Parallel MRI leads to magnitude data corrupted by noise described in most cases as following a Rician or a non central χ distribution. And yet, very few correction methods perform a non central χ 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 χ distributions. We demonstrate on simulated and real data that the extended LMMSE outperforms the original LMMSE on images corrupted by a non central χ noise. © 2011 Springer-Verlag.