Maximum likelihood detection on images

We consider the problem of point target detection on images and focal plane arrays (FPA). Imaging sensors are becoming ubiquitous tools in several applications, such as biomedical systems, autonomous surveillance systems, target tracking systems, and robotics. In these applications, matched filter and template matching are commonly used detection strategies, however, these approaches are unable to provide sub-pixel accuracy and avenues for adaptive pixel-width selection for computationally efficient image processing. In this paper, we derive the maximum likelihood estimator (MLE) of target location on images. The proposed MLE is optimal under the assumption that the FPA contains a point target that has its signal intensity spread in multiple image pixels in the form of a Gaussian point spread function (PSF) with known standard deviation. Further, we derive the Cramér-Rao lower bound (CRLB) of the estimate and present the hypothesis test for target acceptance, resulting in a novel maximum likelihood detector (MLD) for images. Simulation results are provided to validate the performance of the proposed MLE and MLD; it is shown that the MLE is efficient in very low SNR values, starting at -15 dB, and the MLD achieves probability of detection of near unity with zero false alarms starting at 0 dB.