In this paper, we revisit the denoising problem in the context of elliptical distributions; this approach extends a work by Alecu et al. in two directions: (i) we address the multivariate case and (ii) our study is not restricted to the scale mixtures of Gaussians, but extends to the whole family of elliptical distributions. We consider the framework where both the vector to be estimated and the additive independent corrupting noise are elliptically distributed. The MMSE and Wiener filters are computed and their performances are compared in terms of the value of the SNR in several illustrations.