We present the results of a full detector simulation of different types of background to the H rightarrow gamma gamma process. The irreducible background of prompt di-photon production and the reducible backgrounds of gamma + jets production and QCD jet production were investigated. A special goal was to simulate for the first time a large enough sample of the QCD jet background to directly estimate the di-photon misidentification and compare it with contributions from the other backgrounds. The isolation tools are important tools in separating the signal process from the background processes. Using isolation criteria based on information from the PbWO_4 electromagnetic calorimeter and the tracker, we were able to reduce the QCD jet background to a level of ~15% of the total background while keeping Higgs selection efficiency reasonably high