DWI filtering using joint information for DTI and HARDI

The filtering of the Diffusion Weighted Images (DWI) prior to the estimation of the diffusion tensor or other fiber Orientation Distribution Functions (ODF) has been proved to be of paramount importance in the recent literature. More precisely, it has been evidenced that the estimation of the diffusion tensor without a previous filtering stage induces errors which cannot be recovered by further regularization of the tensor field. A number of approaches have been intended to overcome this problem, most of them based on the restoration of each DWI gradient image separately. In this paper we propose a methodology to take advantage of the joint information in the DWI volumes, i.e., the sum of the information given by all DWI channels plus the correlations between them. This way, all the gradient images are filtered together exploiting the first and second order information they share. We adapt this methodology to two filters, namely the Linear Minimum Mean Squared Error (LMMSE) and the Unbiased Non-Local Means (UNLM). These new filters are tested over a wide variety of synthetic and real data showing the convenience of the new approach, especially for High Angular Resolution Diffusion Imaging (HARDI). Among the techniques presented, the joint LMMSE is proved a very attractive approach, since it shows an accuracy similar to UNLM (or even better in some situations) with a much lighter computational load.