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 sep-
arately. 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.