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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 nonlinear generalized (SONG) correlation. The SONG correlation is based on the application of a linear correlation to corresponding binary slices of both the 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 the ones of the reference image when the substitutive noise is uniformly distributed. This is exactly what a particular definition of the SONG correlation does.