Quasi-likelihood Detection of a Finite Image with the Unknown Location and Intensity Distribution

The problem of detecting the heterogeneous image of a spatially extended object observed against Gaussian white noise is considered. It is assumed that the image location and intensity distribution are a priori unknown, but they can be predicted with some error. In order to synthesize the detection algorithm, the quasi-likelihood version of the maximum likelihood method is used. According to this approach, in the expression for the decision determining statistics, the unknown image intensity is replaced with some expected (i.e., predicted) one. Further, the decision determining statistics are maximized over the unknown image location. Subsequently, its maximum value is found, and then it is compared with a threshold selected in accordance with the accepted optimality criterion. To determine the detection quality, the behavior of the deterministic and noise components of the quasi-likelihood receiver output signal in the neighborhood of the real image location is studied. The false alarm and image missing probabilities characterize the detection process, and, in this study, they are determined by means of the local Markov approximation method. The heterogeneity of the received signal, as well as a priori ignorance of its intensity distribution, influences the detection quality. It is demonstrated by the case of receiving a rectangular image with linearly varying intensity while an image with homogeneous intensity is expected.