Weighted myriad filters in imaging

This paper introduces the new class of myriad filters to image processing applications. Like the mean and median filter families, myriad filters emerge as maximum likelihood location estimators. In this case, however, the underlying statistical models are alpha-stable which are much broader and flexible than the rigid Gaussian or Laplacian models associated with mean and median filters, respectively. Consequently, myriad filters enjoy efficiency, robustness, edge-preservation, and edge-enhancing properties. Alpha-stable processes include Gaussian processes as a special case and in general satisfy a Generalized Central Limit Theorem that makes them appropriate for modeling physical phenomena. We develop methods to optimize the filter's weights and we show that the attained results consistently outperform linear FIR and weighted median filters in image processing applications.