Polynomial weighted median filtering

Polynomial filter theory methods are able to approximate important classes of nonlinear systems. In the impulsive noise environments, however, outliers are amplified by the polynomial structure, yielding poor performance. Median filters are well-known for their impulsive noise suppression and fine-detail preservation. In this paper, we extend the weighted median (WM) filtering to a polynomial class, polynomial weighted median (PWM) filters which exploit higher order statistics while being robust to outliers. The PWM filter class is motivated by a study of the statistics of cross and square terms. The breakdown probability for the PWM is given and weight optimization is presented. Finally, the effectiveness of the PWM filter is shown through simulations.