Detecting the faint emission of a secondary source in the proximity of the much brighter one has been the most severe obstacle for using direct imaging in searching for exoplanets. Using quantum state discrimination and quantum imaging techniques, we show that one can significantly reduce the probability of error for detecting the presence of a weak secondary source, especially when the two sources have small angular separations. If the weak source has intensity ε≪1 relative to the bright source, we find that the error exponent can be improved by a factor of 1/ε. We also find linear-optical measurements that are optimal in this regime. Our result serves as a complementary method in the toolbox of optical imaging, with applications ranging from astronomy to microscopy.