Minimum-error-probability receiver for detecting a noisy target in colored background noise

Abstract

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 hypothesis testing with unknown parameters. Both white noise and colored noise are considered to model the additive noise on the target. We show that the solution for the optimum receiver, when the additive noise is 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 second 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 utilized to process the input signal.