Adaptive alpha-trimmed mean filters based on asymptotic variance minimization

Alpha-trimmed mean filters are widely used for the restoration of signals and images corrupted by additive symmetric noise. They are preferred when the pdf tail length is between that of Gaussian and Laplacian distributions. The design problem of these filters is nothing but selecting its only parameter, α, optimally for a given noise type. In this paper, we present an adaptive alpha-trimmed mean filter, which selects α that minimizes the sample asymptotic variance estimate, V_n, of the alpha-trimmed mean estimator. This is an extension of Jaeckel´s proposal of optimal alpha-trimmed mean estimators to signal and image filtering. The simulations that use moderate sample sizes to compute V_n produce promising results