The contribution of this talkis 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.

This presentation is part of Minisymposium “MS10 - Advanced optimization methods for image processing (2 parts)”
organized by: Marco Prato (University of Modena and Reggio Emilia) , Ignace Loris (Université Libre de Bruxelles) .

Authors:

Gabriele Steidl (University of Kaiserslautern)

Friederike Laus (Technische Universität Kaiserslautern)

Fabien Pierre (Université de Lorraine)

Keywords:

cauchy noise, image enhancement, image reconstruction, maximum likelihood estomatoer, nonlinear optimization