An approximation of the GLRT for real time muon detection

The problem of detecting muons in a particle detector is considered. The tracks of high momentum muons can be considered as straight lines, and thus well known techniques for line detection, such as the Hough transform, can be used. In this paper, we show that the Hough transform, which is commonly used in High Energy Physics, can be interpreted as an approximation of the Generalized Likelihood Ration Test (GLRT). We consider the case of a muon detector which consists of a set of sub-detectors, where each sub-detector provides a random activity measurement. Using the probability density functions of these activity measurements, a GLRT for muon detection is calculated, and its performance - when approximated by the Hough transform - is demonstrated.