Maximum likelihood for target location in the presence of substitutive noise

We consider the optimal likelihood algorithm for the estimation of a target location when the images are corrupted by substitutive noise. We show the relationship between the optimal algorithm and the sliced orthogonal nonlin ear generalized (SONG) correlation. The SONG correlation is based on the ap plication of a linear correlation to corresponding binary slices of both th e input scene and the reference object with appropriate weight factors. For a particular case, we show that the optimal strategy is a function of only the number of pixels for which the gray values in the noisy image match th e ones of the reference image when the substitutive noise is uniformly dist ributed. This is exactly what a particular definition of the SONG correlati on does. (C) 2001 Optical Society of America.