Weighted Myriad Filters - Nonlinear Signal and Image Processing: Theory, Methods and Applications - page 191

FIGURE 5.15
(a) Linear blind equalization, (b) myriad blind equalization.

5.11 Conclusions

Weighted myriad filtering is a flexible filtering framework that derives im-
portant robustness properties from the impulsive characteristics of symmetric
α -stable distributions. In the same way that linear and median filters are re-

lated to the Gaussian and Laplacian distributions, respectively, myriad filter
theory is based on the definition of the sample myriad as the maximum like-
lihood location estimator of the Cauchy distribution—the only non-Gaussian
symmetric

-stable distribution for which a closed-form density is available.
When weights (especially real-valued ones) are introduced in the definition,
the weighted myriad filters appear as a rich and flexible class of filters that can
range, by simply varying a tuning parameter, from highly robust mode-like
filter forms to simple and Gaussian-efficient linear FIR filters. This chapter
incorporates the latest developments on weighted myriad filters including
algorithms for fast calculation, filter design, and optimization. A complete

α