Optimum receivers for pattern recognition problems with nonoverlapping target and background noise

Abstract

Optimum receivers for pattern recognition with nonoverlapping target and background noise are designed based on binary Bayesian hypothesis testing with unknown parameters. We overview the design of optimum receiver to detect a noisy target with unknown illumination in nonoverlapping colored background noise. Both white 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 that 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. We discuss two special cases: when the additive noise is zero and when the background noise is zero. We show that when the additive noise is zero, the optimum receiver is independent of the background noise statistics. For the special case of zero background noise, the optimum receiver reduces to a matched filter that estimates the illumination of the target.