Hybrid aeroacoustic methods seek for computational efficiency and robust noise prediction. Using already existing aeroacoustic wave equations, we propose a general hybrid aeroacoustic method, based on compressible source data. The main differences to current state of the art aeroacoustic analogies are that an additional decomposition is used to compute the aeroacoustic source terms and their application is extended to the source formulation, based on compressible flow data. By applying the Helmholtz-Hodge decomposition on arbitrary domains, we extract the incompressible projection (non-radiating base flow) of a compressible flow simulation. This method maintains the favorable properties of the hybrid aeroacoustic method while incorporating compressible effects on the base flow. The capabilities are illustrated for the aeroacoustic benchmark case, "cavity with a lip", involving acoustic feedback. The investigation is based on the equation of vortex sound, to incorporate convective effects during wave propagation.