Multivariate Myriad Filters Based on Parameter Estimation of Student-$t$ Distributions
Friederike Laus, Gabriele Steidl · SIAM Journal on Imaging Sciences · 2019
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 the 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 $ u\to 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.