We present a new method for denoising of Diffusion Weighted Images
(DWI) that shares several desirable features of state-of-the-art
proposals: 1) it works with the squared-magnitude signal, allowing
for a closed-form formulation as a Linear Minimum Mean Squared
Error (LMMSE) estimator, a.k.a. Wiener filter; 2) it jointly
accounts for the DWI channels altogether, being able to unveil
anatomical structures that remain hidden in each separated channel;
3) it uses a Non-Local Means (NLM)-like scheme to discriminate
voxels corresponding to different fiber bundles, being able to
enhance the anatomical structures of the DWI. We report extensive
experiments evidencing the new approach outperforms several related
methods for all the range of input signal-to-noise ratios (SNR). An
open-source C++ implementation of the algorithm is also provided
for the sake of reproducibility.