Merging squared-magnitude approaches to DWI denoising: An adaptive Wiener filter tuned to the anatomical contents of the image

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.