Non-standard radionuclides used in PET imaging introduce additional factors into the imaging model that need to be properly accounted for in order to ensure quantitative accuracy. One of these factors is the emission of cascade gamma rays whereby additional photons of different energies are emitted concurrently with the two anti-parallel 511 keV gamma rays. The emission of these cascade gamma rays has no angular correlation to the emission of the two 511 keV photons. Thus the cascade gamma rays produce a background effect similar to that of random coincidences but with different statistics. We present a method for estimating the shape of the cascade distribution using an estimate of the activity distribution and attenuation map in a manner similar to the estimation of single scatter. The estimated cascade distribution and an estimate for the single scatter distribution are incorporated into a new OSEM algorithm to reconstruct an image that is corrected for cascade and scatter. The resulting image has the background effect removed and has better contrast than when reconstructed using the standard OSEM algorithm.