Nonlocal Myriad Filters for Cauchy Noise Removal

Abstract : The contribution of this paper is two-fold. First, we introduce a generalized myriad filter, which is a method to compute the joint maximum likelihood estimator of the location and the scale parameter of the Cauchy distribution. Estimating only the location parameter is known as myriad filter. We propose an efficient algorithm to compute the generalized myriad filter and prove its convergence. Special cases of this algorithm result in the classical myriad filtering, respective an algorithm for estimating only the scale parameter. Based on an asymptotic analysis, we develop a second, even faster generalized myriad filtering technique. Second, we use our new approaches within a nonlocal, fully unsupervised method to denoise images corrupted by Cauchy noise. Special attention is paid to the determination of similar patches in noisy images. Numerical examples demonstrate the excellent performance of our algorithms which have moreover the advantage to be robust with respect to the parameter choice.
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Journal of Mathematical Imaging and Vision, Springer Verlag, 2018, pp.1-31. 〈https://link.springer.com/article/10.1007/s10851-018-0816-y〉. 〈10.1007/s10851-018-0816-y〉
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https://hal.archives-ouvertes.fr/hal-01814104
Contributeur : Fabien Pierre <>
Soumis le : mardi 12 juin 2018 - 18:58:28
Dernière modification le : mardi 18 décembre 2018 - 16:18:26

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Friederike Laus, Fabien Pierre, Gabriele Steidl. Nonlocal Myriad Filters for Cauchy Noise Removal. Journal of Mathematical Imaging and Vision, Springer Verlag, 2018, pp.1-31. 〈https://link.springer.com/article/10.1007/s10851-018-0816-y〉. 〈10.1007/s10851-018-0816-y〉. 〈hal-01814104〉

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