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The contribution of this study is twofold: First, we propose an efficientalgorithm for the computation of the (weighted) maximum likelihood estimatorsfor the parameters of the multivariate Student-$t$ distribution, which we callgeneralized multivariate myriad filter. Second, we use the generalizedmultivariate myriad filter in a nonlocal framework for the denoising of imagescorrupted by different kinds of noise. The resulting method is very flexibleand can handle heavy-tailed noise such as Cauchy noise, as well as the otherextreme, namely Gaussian noise. Furthermore, we detail how the limiting case$\nu \rightarrow 0$ of the projected normal distribution in two dimensions canbe used for the robust denoising of periodic data, in particular for imageswith circular data corrupted by wrapped Cauchy noise.

Multivariate Myriad Filters based on Parameter Estimation of Student-$t$ Distributions