A New Method to Study the Origin of the EGB and the First Application on AT20G

In this letter, we introduce a new method of image stacking to directly study the undetected but possible gamma-ray point sources. Applying the method to the Australia Telescope 20 GHz Survey (AT20G) sources which have not been detected by LAT on Fermi, we find that the sources contribute (10.5+/-1.1)% and (4.3+/-0.9)% of the extragalactic gamma-ray background (EGB) and have a very soft spectrum with the photon indexes of 3.09+/-0.23 and 2.61+/-0.26, in the 1-3 and 3-300GeV energy ranges. In the 0.1-1GeV range, they probably contribute more large faction to the EGB, but it is not quite sure. It maybe not appropriate to assume that the undetected sources have the similar property to the detected sources.