  The contribution of this study is twofold: First, we propose an efficient
algorithm for the computation of the (weighted) maximum likelihood estimators
for the parameters of the multivariate Student-$t$ distribution, which we call
generalized multivariate myriad filter. Second, we use the generalized
multivariate myriad filter in a nonlocal framework for the denoising of images
corrupted by different kinds of noise. The resulting method is very flexible
and can handle heavy-tailed noise such as Cauchy noise, as well as the other
extreme, namely Gaussian noise. Furthermore, we detail how the limiting case
$\nu \rightarrow 0$ of the projected normal distribution in two dimensions can
be used for the robust denoising of periodic data, in particular for images
with circular data corrupted by wrapped Cauchy noise.
