Benefits of position-sensitive detectors for source detection with known background

We address the question of whether or not the directional or imaging information offered by a position-sensitive gamma-ray detector improves the detection accuracy when searching for a source of known shape amid a background of known intensity. We formulate the detection problem as a composite hypothesis testing problem and examine the behavior of the generalized likelihood ratio test (GLRT) in terms of the area under the receiver operating characteristic (AUC). Due to the analytical complexity of the GLRT in this case, we examine its asymptotic properties when the number of detected photons is large. We find that a detector of uniform sensitivity can more accurately detect a source when imaging information is used.