Signal Sequence Detection Given Noisy, Common Background Image Sets

The optimum processing (likelihood functional) is found for a set of M images {Zm = Sm + Y + Nm}, each the sum of a member Sm of a signal sequence {Sm}, due to an object to be detected and its parameters estimated, a sample function Nm of a noise field {Nm}, and a sample function Y of a common background field {Y}. The noise fields {{Nm}} are independent, zero mean, white Gaussian fields, all independent of the background field {Y}; the latter is assumed to be either 1} completely unknown or of known mean and covariance functions with 2) a certain fluctuation property or 3) Gaussian. Three equivalent forms of the optimum processing are found: 1) a summation of generalized matched filterings of the images, 2) a summation of matched filtering of certain generalized differences of the images, 3) a summation of "estimator-correlator" type filterings. The detection performance and optimum signal/image selection under the Neyman-Pearson criterion is given and the singularity of the ({{Nm = O}} and M > 1) case noted. It is shown that optimum processor and signal design can completely eliminate any effect of the background on detectability (M > 1). The Cramer-Rao lower bound for the signal parameter estimates meansquare error is given along with an example; optimum signal/image selection in the single parameter case is discussed.