Addendum to "Sequential anisotropic multichannel Wiener filtering with Rician bias correction applied to 3D regularization of DWI data" [Medical Image Analysis 13 (2009) 19-35]

By means of this addendum we would like to give credit to an important work by Koay and Basser (2006) closely related to one of the results of our paper recently published in this journal (Martin-Fernandez et al., 2009). A key point in the implementation of the filtering approach proposed in Martin-Fernandez et al. (2009) is the inversion of the function BðcÞ given by Eq. (B.11). While the expression for BðcÞ was derived previously by the authors Martin-Fernandez (2001), Martin-Fernandez et al. (2006), an efficient solution for computing c from B was presented independently by Koay and Basser (2006). Handling this function is an important component of the method we describe in Martin-Fernandez et al. (2009), therefore, the above-mentioned paper should have been referred. We would like to stress, however, that our research effort has been carried out, at least, in parallel to that of the authors we here give credit to. Specifically, the function BðcÞ mentioned above had already been derived and depicted in the Ph.D. thesis (Martin-Fernandez, 2001) of the corresponding author of Martin-Fernandez et al. (2009), which was published in 2001 and defended in 2002. The monotonic behavior of this function guarantees that the inverse function exists; whether this inverse is calculated by means