Optimum filter for detection of a target in nonoverlapping scene noise

A filter function is derived for input signals containing a target that is spatially disjoint (that is, nonoverlapping) with the input scene noise. The optimization metric is the ratio of the square of the expected value of the correlation peak to the expected value of the output signal energy. In this model the effects of the nonwhiteness of the scene noise, the nonstationarity of the scene noise that is due to the limited size of the input scene, the nonoverlapping of the target and the scene noise, and the unknown variations of the target illumination are considered. We show that, for the nonoverlapping target and the scene noise, the target window and the scene-noise window strongly influence the optimum filter function.