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arXiv · 1810.05594

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

Friederike Laus·Gabriele Steidl
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Abstract

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 $ν\rightarrow 0$ 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.

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Friederike Laus, Gabriele Steidl. 2019-06-19. Multivariate Myriad Filters based on Parameter Estimation of Student-$t$ Distributions. https://arxiv.org/abs/1810.05594

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