A generalized likelihood ratio test for detecting targets in multiple-band spectral images with improper complex Gaussian noise

A generalized likelihood ratio test is derived for detecting target patterns in multi-band spectral images with improper complex Gaussian noise. The GLR test generalizes previously derived tests, which were restricted to proper complex Gaussian noise. However, this generalization comes for the price of increased computational time. The GLR test is derived based on the joint multivariate pdf of the magnitude and phase of correlated complex Gaussian variables. An expression for the probability of false alarm is obtained which shows that the test achieves a constant false alarm rate. The GLR test was applied to simulation and experimental data and showed satisfying results.