Rank-order filters and Bayes posterior decision

Optimal rank-order filtering under the MAE (mean absolute error) criterion is shown to be equivalent to the a posteriori Bayes decision. It is also shown that finding the minimum MAE ROF (rank-order filter) does not require an LP (linear program), thus dramatically reducing the complexity of the algorithm presented by E.J. Coyle (1988). Furthermore, the median filter is shown to be the optimal solution (in the minimum MAE and the a posteriori sense) for a very practical case. The robustness of the designed ROFs with respect to the cost coefficients is analyzed, which, supported by the independence of the optimal solution on the prior statistics of the signal and noise processes, suggests the potential of ROFs in practical applications