When a target is embedded in random media, the quality of optical imaging can be improved by actively controlling the illumination and by exploiting vector wave properties. A rigorous description, however, requires expensive computational resources to fully account for the electromagnetic boundary conditions. Here we introduce a statistically-equivalent, scaling model that allows reducing significantly the complexity of the problem. The new scheme describes the entanglement between the local wave vector and the polarization state in random media, and also accounts for cumulative properties such as geometric phase. The approach is validated for different scenarios where the coherent background noise alters substantially the performance of active imaging.