Ah. Fazlollahi et al., MINIMUM-ERROR-PROBABILITY RECEIVER FOR DETECTING A NOISY TARGET IN COLORED BACKGROUND-NOISE, Journal of the Optical Society of America. A, Optics, image science,and vision., 14(4), 1997, pp. 845-852
We describe the design of an optimum receiver to detect a noisy target
with unknown illumination in nonoverlapping colored background noise.
The optimum receiver is designed on the basis of binary Bayesian hypo
thesis testing with unknown parameters. Both white noise and colored n
oise are considered to model the additive noise on the target. We show
that the solution for the optimum receiver, when the additive noise i
s white, consists of three terms: The first corresponds to the energy
of the input signal, which is defined as the lexicographically ordered
samples of the input image within the window of the reference; the se
cond is the square of the correlation between the input signal and the
energy-normalized reference; and the third corresponds to the energy
of the whitened input signal. When the additive noise is colored, the
third term is the same; however, the first two terms change such that
the information in the correlation matrix of the additive noise is uti
lized to process the input signal. (C) 1997 Optical Society of America
.