The signal-dependent rank order mean (SD-ROM) filter is effective at removing high levels of impulse noise from 2- D scalar-valued signals. Excellent results have been presented for both a two-state and a multi-state version of the filter. However, implementation of the two-state SD-ROM filter requires the selection of a set of threshold values. In this paper, we propose a method for choosing the thresholds based on a statistical characterization of an input image. The method approximates the histogram of an image with a weighted sum of Gaussian distributions. Using the statistical model and the input distributions, the likelihood of correctly identifying impulses is estimated as a function of the thresholds. By maximizing the likelihood of correct detection, optimal thresholds are predicted. The performance of the algorithm using the predicted thresholds is compared to the optimal performance found using a brute-force search.